Raid boss
Raid bosses are bosses which require a raid to defeat. Typically players only encounter raid-bosses from level 60 and upwards. Their level is often unknown and thus depicted by a skull instead of the level.
Not that alhough each of these bosses have a recommended raid size, they may be done with fewer players. Each boss was tuned for raid group of the size listed at the of their introduction, but new equipment and raised level caps may make the fights easier than they once were.
World bosses
World bosses are by definition bosses who are outdoors. They can be attacked by an indefinite amount of players, though only one group will be able to loot the boss, and usually a group of 40 players in Eastern Kingdoms and Kalimdor and 25 players in Outland should do the trick.
Amongst the most famous bosses are the four dragons of the Emerald Nightmare.
Event bosses
Event bosses are typically outdoor bosses, who only spawn during a specific world event. After this event, the bosses will no longer be available.
The most memorable event which spawned raid bosses was no doubt the opening of The Gates of Ahn'Qiraj.
Quest bosses
Quest bosses are bosses who are spawned as the result of a quest or quest-chain. These can be both non-repeatable (long and epic quest-chains) as repeatable (reputation-quests).