The Heavy has two main weapons, a big machine gun and a rocket launcher. He excels at laying down suppressive fire and destroying cover, in addition to dealing big one shot damage.
Burst of Steel – Firing in XCOM usually means the end of your soldier's turn, but with Burst of Steel if you stand still and fire you can take a second action. That action can be to move, reload, go into overwatch or even fire twice for maximum dakka.
Suppression – Suppressing fire is a special kind of shot. It doesn't do any damage, but it does reduce aim, destroy cover, and grant you a reaction shot if your target moves. It's a very useful weapon in your armoury, especially if the enemy is stupid enough to hide behind something explosive.
H.E.A.T. rounds – Doubles your damage against robotic enemies. This ability may not seem useful when you first get access to it, but two of the strongest enemies in the game, Cyberdiscs and Sectopods, are robotic, and this really helps you deal with them.
Assaults are the guys who get up close and shotgun the enemy in the face. Their signature move is Run and Gun, which lets them move twice and still fire or go on overwatch.
Lightning Reflexes – One of my favourite perks in the game. Lightning Reflexes forces the first overwatch shot against your soldier to miss. This not only keeps him alive and lets him close in on the enemy, but can be used to clear the way for the rest of your soldiers.
Close Quarters Fighting – Grants a reaction shot against anyone who approaches within four squares of the assault soldier. I've lost count of the number of times this has saved my ass from being injected with Chyssalid eggs.
Rapid Fire – Fires a double shot, but at reduced accuracy. At close range this can be devastating, and if you use a pistol, it works at a distance too. There's also a second reason to get it, it's counterpart, Flush, is far less useful, and often doesn't seem to work at all.
Snipers can do massive damage at range, capable of taking out even tough enemies like Mutons with a single shot. But they can't move and shoot with a sniper rifle, and struggle to hit enemies up close.
Snap Shot – Lets you move and fire with a sniper rifle at reduced accuracy. The choice between this and Squad Sight (shoot anyone any soldier can see) is a hard one, but the latter is often foiled by inconvenient walls, while Snap Shot lets your sniper keep pace with the rest of the squad and still be useful.
Battle Scanner – An overlooked skill, since it's one of the few Sniper abilities that doesn't involve shooting people. Tossing this scanner reveals part of the battlefield, including any enemies nearby. However it does so without alerting the enemies to your presence, meaning they don't scramble for cover.
Opportunist – Removes the accuracy penalty for overwatch attacks. This lets a Sniper climb to high ground and cover the entire squad with ease. Opportunist helps compensate for the aiming penalty for Snap Shot, or pull off some amazing trick shots with Squad Sight.
Supports are one of the most versatile classes in the game. They use standard rifles and can toss smoke grenades, but their main draw is their superb medic abilties. I usually take two Supports per squad, they're that useful.
Field Medic – This incredibly useful ability allows you to get three uses from every medpack, turning your support into a roving medic. It's an absolute must have, the best way to keep your squad on their feet throughout the mission.
Revive – The second strong medic ability in the support tree. This one means that critically injured squad members can be revived instead of merely stabilised, because nothing can stop an XCOM soldier from kicking alien ass.
Deep Pockets – Every Support gets this ability at Major, but it's worth pointing out just how good it is. It allows you to take two inventory items instead of just one. Letting you carry a grenade or protective vest in addition to your standard medpack.
When a soldier is found to have psychic powers, they unlock a second, smaller skill tree. Using these powers grants you the experience to climb that tree, making your best soldiers even more potent.
Mindfray – The one ability every psychic has. It deals five damage and reduces the target's aim, willpower an mobility. It's extremely accurate over long range, kills weak aliens quickly and sets up tougher ones for other mental attacks.
Psychic Inspiration – Finally! A way to stop those weak willed rookies from panicking and shooting their pals. Psychic Inspiration removes panic and Mindfray effects and boosts willpower, a massive boost to your men's resolve.
Mind Control – The power you've finally been waiting for. Mind Control lets you pull the same tricks as Sectoid Commanders and take control of the enemy units. Sadly, your version isn't as effective as theirs. The aliens have several units that are immune to or resistant to psychic powers, and will happily shoot down their own soldiers before you can use them much. It's still incredible fun when you pull it off though, especially when paired with Mindfray to lower their defences.