There are 18 "canned" character classes. These classes have set skills, benefits and restrictions. The classes basically break down into three categories: spell slingers, skull crushers, and sneaks (or "mages", "warriors" and "thieves"). Most combine skills of two or more of these categories, except the Monk which is pretty much in a class by itself. You will frequently encounter all but two of these classes as opponents over the course of the game. The two classes you will probably not encounter very frequently are the Acrobat and Healer. This is either Bethesda's way of telling you that these two classes lack serious offensive capabilities or a malfunction of the random critter generating subroutine.
Race may affect pre-made classes more than Custom Classes. I've included the information on race provided by Bethesda, but do not vouch for its accuracy.
The following links will bring up a table that gives the skills, benefits, restrictions, max hit points, stat changes, and comments on the development and play of the character class. Starting spells include those which are generated by the background questionnaire. Your starting spells may be slightly different depending on how you answer the background questionnaire.
Mage
Spellsword
Battlemage
Sorcerer
Nightblade
Bard
Burglar
Rogue
Thief
Assassin
Monk
Archer
Ranger
Barbarian
Knight
Warrior
Acrobat
Healer