Warriors
The reaver is a 2 button class Dragon's Rage is just superior to anything a warrior has access to and if you use heal on kill items +healing crafting and devour you can destroy everything and remain at low health doing extra damage. It is very strong but monotonous after a time. I hear going S&S instead of 2H improves the experience a lot but I have yet to try it.
The templar is basically your base warrior that has access to a lot of useful team buff and a huge burst every now and then and is of the very few classes that can prime and detonate cross class combos on its own. In combat the Templar fills the support-ish role but is still viable for either tanking or dps (either 2H or S&S). It also performs exceptionally well against demons.
The champion is the most defense oriented spec of all the warriors and as such is more suited to S&S (none of your champion skills is weapon damage based). As a champion you are virtually invincible and To the Death makes boss fights a lot easier. I had some fun playing S&S champion but I really like tanking. The champion spec add the least to the playstyle of warriors.
Rogues
The assassin has the highest single target dps of all the classes. Viable as dual wield and archer (although the spec favors dual wield a bit more) I had a blast playing assassin. It relies on very heavy stealth play as you reset your stealth cooldown with each kill. So the playstyle would be something like stealth-burst 1 target down-stealth repeat. In my opinion it is the most rogue-ish of the specs. Finally while the assassin can completely destroy almost everything in the game it is very fragile a lot more than the tempest and thus has to remain very mobile moving from target to target all the time. That makes a very powerful and engaging class to play. I found it is also incredibly rewarding if played right.
I don't have much on the artificer since I have yet to play it but here is my two cents.
The artificer for some people is the most fun of all the rogue specs. More viable as an archer by a rather large margin (it lacks active skills in the spec) the cooldown reduction passive you get on your teams critical hits allows to you effectively spam your skills resulting in very high damage (still not as high as the assassin's) while providing your team with a lot of helpful buffs. With a high critical chance team you can't go wrong as an artificer.
Mages
The knight enchanter if you haven't already seen the countless posts here on this very forum is considered the most broken class in the game. Reason for that is a talent that allows you to generate barrier based on your damage making you almost impossible to kill even on nightmare. For the playstyle this is where things gets wrong since you can play the class with 3 buttons. The whole spec is based on the Spirit Blade and as such suffers the same way as the reaver. It becomes incredibly dull and boring after a time.
The rift mage works almost the same way as the artificer. You get a skill set that allows you to weaken enemies reducing their damage by (I belive) a whooping 30%. Pretty sweet right? well we are not done yet as all damage you do on weakened targets restores your mana. This allows you to have virtually infinite mana for as long as the weakened status is up. In combination with some of the other mages talents you become a turret of devastating spells. The most important thing the rift mages offer though is control. As a rift mage you have absolute control over the battlefield with a rather large set of control abilities. The rift mage is also the best combo class in the game.
Unfortunately I have nothing on the necromancer although I hear the high mana cost of the spells diminishes the fun factor of the class. Take that as you will.
Good luck.