(I wrote this up for the folks at Deep Space, but thought I'd share it here as well. This is just meant to be an overview; certain upgrades, some Forgeworld variants and other goodies aren't covered)
There are many tanks available to many armies in the Warhammer 40k universe, but few can compare with the powerful resilience and offensive power of the Eldar skimmer tanks. Combining terrible offensive capacity with fearsome defenses, tanks such as the Wave Serpent or Falcon easily stand as the fastest, most terrifying battle vehicles available in the game; just ask any foe of the Eldar who has had to contend with them.
The first universal rule of using Eldar skimmer tanks is that you must always make sure they move more than 6" per turn. In doing this you can take advantage of the rule which denies your opponent anything but a glancing blow if they should successfully land a shot on you and punch through your armor. There are down sides to fast movement, however; speed means that an immobilized result will instantly destroy your tank (as you are moving so quickly that being immobilized makes you crash) and if you *are* destroyed then any passengers will be twice as likely to take a wound (as you re-roll to-wound rolls for passengers traveling in a fast vehicle that is destroyed), but there are tank upgrades which mitigate these effects, and they'll be described later. In short: Keep moving. It's worth whatever additional risks might come with the speed. We'll get back to this.
Worth noting: Any skimmer that is attacked in hand-to-hand can only be hit on a roll of 6 (which frustrates a lot of Tyranid players, I can tell you).
Putting the question of speed aside for the moment, one of the first things that you'll notice about Eldar tanks is that they have amazing firepower. This is because of 4th ed rules which allow a fast skimmer to move up to 12" and fire one offensive weapon (defined as strength 7 or more) and all defensive weapons (strength 6 or less). Eldar grav tanks are outfitted in such a way that this rule plays utterly to their favor. For instance, a Wave Serpent can be stocked with a twin-linked offensive or defensive weapon and can take a Shuriken Cannon as well, and is thus equipped to fire everything the tank is armed with so long as it doesn't travel more than 12" in a turn. The Fire Prism has a powerful Prism Cannon and can also take a Shuriken Cannon... thus giving it the ability to fire all weapons in a turn as well if it moves less than 12". Every Falcon is stocked with a pulse laser, can take a Shuriken Cannon if the player wishes, and can also add another heavy weapon. If that heavy weapon is Str 6 then, like the Wave Serpent, the tank can fire everything it carries if it moves up to 12" (if that second heavy weapon is greater than str 6, like an Eldar Missile Launcher or a Bright Lance, then the player no longer has the option as those are not "defensive" weapons). Obviously, the Falcon can be a very, very potent gunboat which mows through infantry with ease.
As you can tell from the above-mentioned statistics, taking a Shuriken Cannon and another Str 6 weapon (such as a Starcannon, Scatter Laser or additional Shuriken Cannon) can maximize the number of shots that a Falcon fires in a single turn, but it comes with a hitch; those shots will primarily be for light tank hunting and infantry. Though the Pulse Laser can do more damage to a heavier tank (due to its high strength rating), using it in this way means the other two heavy multi-shot weapons are wasted. Ultimately this means you've spent points on guns you won't use. Taking a second weapon capable of cracking stronger tanks (such as a Bright Lance or a Missile Launcher) won't increase the number of anti-tank shots either, as you cannot fire more than one offensive weapon once you've traveled over 6". As stated above, one must always keep moving more than 6" in a turn, so the option of staying still to blast away isn't such a smart one, especially considering that you can shoot all you want is you select your weaponry well.
Another reason why you will want to outfit your Falcon with multi-shot, str 6 weaponry for anti-personnel purposes is because of its ballistic skill (3). With only a 50% chance of hitting, you want to make sure you fire as many times as you can so that you land the most hits. This is one of the main weaknesses in the Fire Prism's design; the 50-50 chance of landing a single shot every turn means you waste that entire huge cannon blast if you get a single roll of 3 or less. Getting back to the Falcon, however, it is clear to see that you can release a hail of gunfire from it if you trick it out with lots of multi-shot weaponry (for instance, a Falcon armed with a Shuriken Cannon and Scatter Laser in addition to the Pulse Laser can score as many as 12 str 6 shots in a single turn if your rolls are lucky).
The Fire Prism is a bit of a hit-or-miss choice, in the literal sense of the word. Armed with a single weapon of Str 9, AP2, blast statistics, it can do major-league housecleaning against tanks and infantry alike. It also carries the Shuriken Cannon upgrade if the player decides to take advantage of it, but when one takes the Fire Prism, it's primarily to strike from a distance which makes the Shuriken Cannon unusable. It's hard to say how a Prism Cannon is supposed to compare with other Eldar weapons such as the Missile Launcher or Bright Lance. On the one hand, it does have a high strength rating, but it's advantages over other heavy weapons is negligible. What's more, the Prism Cannon is not twin-linked and, aside from the Shuriken Cannon, it's the only heavy weapon the tank can carry (it also cannot transport passengers). This becomes particularly relevant due to its Ballistic Skill of 3, which translates into a 50% chance of wasting that powerful cannon shot, while other vehicles offer a little bit of consolation if you don't hit with your first roll. If you're going to take a Fire Prism, make sure you are doing it with a specific plan in mind.
The Wave Serpent also carries a Ballistic skill of 3, but its main offensive weapon is always twin-linked. Unlike the Fire Prism, this increases the likelihood of landing an offensive weapon's shot to 75% (because missed shots can be re-rolled). It also differs from the Falcon in that a Wave Serpent can only take a single offensive weapon and a shuriken cannon (lacking that third heavy weapon the Falcon enjoys). This means that you aren't going to be raining a lot of shots into enemy ranks, so why not go with higher-strength shots like a Bright Lance or Missile Launcher? The re-rolls make missing less likely, thus making a Wave Serpent a great anti-tank gunboat. The Shuriken Cannon does little to aid in the hunting of heavy tanks, so a lot of players don't even bother (deciding to dedicate the Wave Serpent to a single job), but it's up to the player to determine if it's good to have a little extra firepower. You never know when your enemy is going to blast one of your guns off and you'll need a backup!
Eldar Wave Serpents enjoy some interesting benefits from the fact that they are troop transports as well as full-on tanks in their own right. A Wave Serpent can carry a squad of troops or elites in numbers limited from 6 (for Wraithguard accompanied by a Warlock) to 10 (for most regular infantry). When a this vehicle wants to make a strong assault on a squad or vehicle, it can move within range of the enemy and (if it hasn't traveled more than 12") disembark passengers who can then fire their weapons to support the tank's attack. Naturally the passengers who rode in the Wave Serpent to the destination fire under the limitations of a moving unit (i.e. heavy weapons cannot be used in that turn). Additionally, all disembarking passengers cannot assault until the next turn, so be careful with those Scorpions and Banshees. Even so, a squad of Fire Dragons, Wraithguard, Dire Avengers or even Defender Guardians can unleash a withering hail of fire and, if the player wishes, can even target a different enemy unit than the Wave Serpent does. If executed cleverly, the combined firepower of the tank and the infantry unit can mow difficult opponents down before they have a chance to respond.
Falcons can also carry passengers (though only six regular infantry; no Wraithguard!) and can benefit from the support in the same that Wave Serpents can. It's common for Eldar players to put small units of very heavy shooters (like Fire Dragons or Storm Guardians armed with Fusion Guns) in a Falcon for on-the-spot firepower where it's needed.
The Wave Serpent has a unique defense in the form of an Energy Field on the front and sides that reduces enemy fire stronger than str8 to 8. Due to the armor rating of 12 on the front and sides of the Wave Serpent, this means that an enemy will always need to roll at least 4 or more to score a glancing hit, regardless of what the weapon's strength actually is. Smart enemies will know this and will rarely waste weapons stronger than S8 on the skimmer, but some armies (such as Tau) depend on their S9-S10 weapons to gain an advantage, and the Eldar Wave Serpent takes that away from them. Only the Wave Serpent and the Eldar War Walker come standard with this defense and is likely part of that vehicle's design as a compensation for them not being able to take the valuable Holo-Field upgrade (described below).
As if the Eldar tanks weren't powerful enough, they enjoy upgrades and powers that skimmers from other armies do not. Eldar players should seriously consider using two upgrades in particular to protect their vehicles: Spirit Stone and Holo-Field. These three upgrades can make the destruction of an Eldar tank an extremely difficult task.
Spirit Stone is an upgrade which confers dramatic benefits to a tank once it's been struck. When the enemy scores "Crew Shaken" or "Crew Stunned" results on the damage table, the Eldar player rolls a D6. "Crew Shaken" results are shrugged off on a roll of 4+, and "Crew Stunned" results are downgraded to "Crew Shaken" on a roll 4 or 5, and ignored completely on a roll of 6. Seeing as an Eldar player can easily limit the enemy to Glancing Hit results (by moving the vehicle more than 6" in its turn), this makes Eldar tanks harder to stop or slow down. This is especially valuable, because once a Skimmer is stunned (i.e. can't move), it allows the enemy to attack again in hopes of scoring a penetrating hit, as the tank will not have moved over 6" (in fact, it will not have moved at all).
A more expensive upgrade (25 points) is called Holo-Field, and it is also more dramatically effective (note: this upgrade not available to Wave Serpents). When an enemy rolls on a damage table, they must roll two dice and take the lowest results. On its own, the Holo-Field upgrade stymies the enemy attempts to quickly dispatch the Eldar vehicles, but when used in combination with other upgrades, this upgrade really shines.
The true measure of the magic in these upgrades can be appreciated while watching them in action: An enemy fires a powerful weapon, such as a Rail Gun, at the Eldar tank. If the tank has moved more than 6", the enemy weapon can only achieve a Glancing Hit, regardless of its roll. Furthermore, if the vehicle is a Wave Serpent that weapon will count as being S8 rather than its usual S10 (unless the opponent shoots from the rear), but armor penetration for Falcons is calculated normally. Assuming that the enemy manages to roll penetration equal to or better than the Eldar tank's armor, they must then roll on the Glancing Hit table. If, however, the tank is equipped with Holo-Field, they must then roll two dice and select the lowest results. Given that the Spirit Stone upgrade has a 50% chance of reducing or eliminating any "Crew Stunned" or "Crew Shaken" results (which make up 50% of the Glancing Hit damage table), the enemy must roll greater than 3 on both dice to bypass that upgrade's effects. If the enemy rolls a 4 and destroys a weapon (which weapon the tank loses is the attacker's choice) there's nothing to prevent the loss of a Pulse Laser or a twin-linked Bright Lance. On the other hand, Eldar tanks that have taken the Shuriken Cannon upgrade will still have at least one heavy weapon to fall back on and the tank will still be a formidable enemy, so unless the Eldar player has a lot of heavy vehicles to destroy, losing that armament is a light loss. When all is said and done, the enemy will only do serious damage if their roll is 5 or better on both dice (5 is "Vehicle Immobilized" and 6 is "Vehicle Destroyed"), and if the Eldar tank hasn't moved 6" or more in that turn the enemy really needs a 6 on both dice to make a lasting impression and take that tank out of the equation.
Many players apply these upgrades and tactics not only to tanks, but to Vypers as well. While Vypers have a lower armor rating than Eldar tanks (10 instead of 12), they can enjoy the same upgrades and, in some ways, accomplish even more due to the fact that they can be fielded in twos or threes and have a lower points cost. Vypers are more vulnerable, however, in that they are open-topped, which gives enemies a bonus for damage and using ordinance weapons against them. That being the case, Vypers remain a fairly inexpensive way to assassinate enemy vehicles and infantry (with the option to take a single weapon of any strength and a Shuriken Cannon upgrade). In the mean time, Wave Serpents can transport infantry to strategic locations and Falcons can mow down enemy troops with aplomb.
It's easy to see why an Eldar player would choose to field as many vehicles as possible; no army can match the Eldar maneuverability, defensive upgrades and weapon options. Many players choose to field vehicles with a minimum of upgrades in order to save points for more infantry and more vehicles, and this approach is not without merit. If you are reluctant to sink so many points into your vehicles, you may wish to deploy one heavily upgraded skimmer tank along with a few with a bare-bones configuration and see how they compare. On the other hand, one souped-up Falcon will normally soak up more enemy fire than three Falcons without upgrades, and every turn your vehicles survive is a turn in which they can do more damage. There are a lot of powerful enemies out there; use every fair advantage you have to see their arrogant smirks melt away when they throw everything they've got at you and you're still in the game anyhow.