I'm about to start a Dungeons and Dragon 3.5 adventure, and the last time I created a character I didn't feel there were many options to choose from (unlike Dungeons and Dragons, 4th Edition). What playable races and starting classes are available in Dungeons and Dragons 3.5?
There are lots, too many to list here, and it will depend on which books the game has available for use and if things like LA are allowed. There is a (mostly complete, last updated Oct 2007) list of races (PDF) along with book references, collected by Chet Erez.
There is also a similar (to Feb 2007) index of base classes (PDF) that also includes variants, also collected by Chet Erez.
Every source for every class. Many classes are listed repeatedly since they can be found in multiple books (Eberron Campaign Setting and Forgotten Realms Campaign Setting each discuss all the core classes and how they exist in those settings, for example), but the list should be absolutely complete. As you can see, there are a lot, and there are several times as many prestige classes as base classes.
There are no official lists of playable races; Wizards only has a more general monster index. Chet’s index is very useful, but not totally complete.
The Master 3.5 Playable Race List should be pretty close to complete, though, being a community effort updated steadily over time. It only lists LA +0 races (i.e. no monstrous or "powerful" races), but links to a pretty good list of LA +1 and +2 races. Races with an actual LA (i.e. not LA –) are playable under the rules, but in practice become increasingly unplayable as more LA is added; even +1 or +2 is extremely problematic.