City of Heroes Archetypes
The AT you choose will determines what kind of powers you will have and what your major style of gameplay will be. Here is a quick summary of the typical role each AT (a section on powers follows):
Tanker
Their job is to hold Aggro and survive as best they can while the rest of the group beats the tar out of whatever enemies are around. In short, their job is being tough. A tank will take a bat to the knee, a gunshot to the chest, and an axe to the head while his player is off taking a potty break with no problems.
Note that playing Solo can be slow because of the low damage that most tanks do, but since dying is more rare (especially at high levels), Tanks rarely have to make frequent trips back and forth from the hospital to a tough mission.
Auto-power: Guantlet - Every time you hit an enemy, it and surrounding enemies are hit with a light Taunt effect. This fits very well with the tank philosophy of "Hey! Bad guy! Leave those squishies alone". All you have to do is keep switching targets to keep them fully occupied on you.
Blaster
These are the mass destruction characters of the game. They are often the Pullers because of their long range attacks and they're good for nailing flying foes, one's stuck in the ceiling, or Runners. They also have the most AoE damage which is very fun, but also dangerous in that it draws Aggro from anyone else (like the tank) directly to you. Being extremely Squishy, it's important to use hit-and-run tactics, use the terrain to prevent being overwhelmed, or use the strengths of team members to stay alive.
Balancing the massive ranged power of the blaster without getting killed can be challenging and many people don't do it well. I have often teamed with blasters who really helped the team and were critical to the success of missions and TFs, while other times, vast pain and agony were the result of teaming with a "bad" blaster. The key is to be careful about the blasters on your team. A dumb tank will only get themselves killed while a dumb blaster will get everyone else killed.
Auto-power: Defiance - As you lose life, you gain damage potential. I find this power to be nearly useless because if you're almost dead, it's because something's killing you. You're not likely to dish out much damage before taking a dirt nap. Also, if the healers are doing their job, you'll be healed again in a second or so which destroys your defiance meter. Not a very useful power in most cases.
The only time I've actually seen this be useful is if you barely survive an attack when there's only one or two enemies aggroed to you. Instead of running, you can basically flick your finger and kill them, but you have to do it FAST (before their next attack) or you're toast.
I believe that many of the times that Blasters die is when they're desperately trying to use Defiance by blasting everything in sight when their life is low hoping to kill them first.
Controller
Crowd Control. With a strong controller, it's possible to be effective without a tank because the enemies will be frozen, confused, held or whatever. This can be dangerous though. Because Controllers have low damage output, they can't kill a huge crowd before the holds wear off. Therefore, if they try to take on too many solo, it can get them into trouble. Likewise, if the team they're with doesn't fully take the aggro by the time the hold wears off, the entire room of bad guys will come looking for the 'Troller.
Auto-power: Containment - As far as auto powers go, this is one of the most useful. A controller automatically doubles damage dealt to any enemy that is under a control power's effect (such as holds, slows, confuse, etc.). Since controllers want to fire control powers before attacks anyway, it's a perfect power for them.
Defender
The Everything Character. I really like defenders because they have a good balance of attack/control and healing/support powers. A defender helps the team by altering the rules of play. Defender powers can provide team protection, weaken the enemy, provide healing, improve the stats of other players temporarily etc.
For example, one time while fighting a high-level Psionic powered AV, my team found that he did about half damage with me around because of the defense bonus my character added to the team and the accuracy pentalty I applied to him.
It's interesting to note that the controller's secondary powers are the primary power sets for defenders. Because of this, there can be a lot of overlap in the duties of controllers and defenders, but generally, controllers are crowd control/team support and defenders are team support/enemy manipulation.
Auto-power: Vigilance. As team member's life totals fall, a defender uses less endurance. This is very useful IF you're on a team and IF they're dying. In general, this is a fairly so-so power.
Scrapper
High damage, medium hit points. The scrapper's primary job during a team battle is to add damage to what the tank does and take out the problem enemies quickly. They are strongest when fighting one or two enemies at a time, but can dish out more damage than anyone (even blasters) to a single target. Because they are also decently tough, they can take enemies far above their level.
It should be noted that for people who either don't have the skill or the desire to worry about other team mates or complications like Aggro, Scrappers make a very good first character. This is also good for impatient people who just want to get out there and kills stuff.
Auto-power: Critical Hit. A portion of scrapper attacks will be critical hits which do double damage. Because of this, taking powers that hit multiple time such as Dark Maul (for Dark Melee scrappers) or Flurry (from the speed power pool set) will give you better chances for landing criticals.
Kheldians( 
Peacebringer / 
Warshade )
These odd character types are often seen as flying squid-like things. Each type has a large amount of abilities to choose from (far more than the other ATs, though I think all types should have this many powers or more), and some very cool inherent powers.
To play one, you first have to have at least one of your other characters on any server at level 50.
Of note are the three major forms: human, nova, and dwarf. Human is normal and has the most variety of power while nova is the flying form I talked about before. Novas have great attack but no defense. Dwarfs are large bulky looking things that look more like giant lobsters and have the characteristics of a tank. Because of this, Kheldians have some of the best versatility as far as team members go
Auto-power: Depending on the team member archetypes that are with a Kheldian, they gain bonuses to attack, defense, and resistances. For this reason, Kheldians benefit by joining a team of diverse archetypes. Also, Peacebringers have Fly from level 1 and Warshades have Teleport.