Fallout 3

Well there's different ways to answer this.

There's two quests in the tutorial.

There are 11 main quests and about 17 side quests.

But there are also on-going quests that don't really have an end.

Such as giving Pre-war books to a scholar of the Brotherhood of Steel for money and xp. As long as there are Pre-war books in the game the quest is active.

well not really, at the end there IS or should be an end to the books quest because there is a limited number of them (98) and i agree with the number of quests that rob_indahood said but i doubt that the turning in fingers or ears quest ends (if it is considered a quest)

I recommend you check out http://fallout.wikia.com/wiki/Fallout_Wiki and look under Fallout 3 - Quests

But so you know, the number of quests is growing due to new downloadable content, the latest being Operation Anchorage.

Have fun

There are 11 MAIN quests and 17 SIDE quests in the regular game, 4 quests in the Operation: Anchorage DLC, and there will be 4 more quests in the upcoming "The Pitt" DLC coming out March 24.

Alot of them 11 main that i kno of......i dont have the manual for all of the sec. quest but iv'e done a good deal of them.

I have completed 45 quests total, thats with the Pitt, Anchorage, and Hard Steel DLC
So far i havent found any more, thats doesnt include undocumented (pre-war books/sugar bombs/scrap metal),or random encounter mini-quests

i have completed 40 and thats including the new point lookout so there you go
(these are the only ones that you get GP for)

See here for more information: fallout.wikia.com/wiki/Fallout_3_quests

With all of the dlc downloaded there is approx 40 quests altogether.

Without the expansions there are 30 major quests.