Fallout 3 quests

General information
Every quest that appears in your Pip-Boy grants an achievement (on Xbox 360 and PC) or a trophy (on PlayStation 3) upon completion in base game only. Unmarked quests do not provide achievements/trophies. Side quests in Point Lookout and Broken Steel do not provide achievements/trophies either.

Most of the quests in Fallout 3 either involve or can be completed with a combat situation (e.g. killing Vance and The Family in Blood Ties).

There are 59 quests (main, side and repeatable) in the base game. The 5 add-ons provide for a further 35, which makes the total 94 quests.

Main quests
Main quests with names in italics can be skipped through a speech check. This is one of two ways to skip Galaxy News Radio (other than through unintentional glitches), the second way to skip through Galaxy News Radio is by going directly to Rivet City, Rescue from Paradise can also be skipped through use of Child at Heart to convince Robert MacCready to let the player character into Little Lamplight. Both quests can then be completed as a side quest at any time.

All quests up to Tranquility Lane can be skipped by finding and entering Vault 112. Doing so may cause some bugs and glitches. Another way is to glitch your way into the Citadel and find the Vault Locations Computer in the A ring. Doing so will skip you to the Picking Up the Trail quest and may cause a very large number of glitches.

Unmarked quests
Aside from the major quests listed above, there are a number of minor ones that are not listed as quests in your Pip-Boy. They don't count as achievements or trophies either.

Repeatable quests
Some characters want specific items. These can be repeatedly given for XP, caps, or Karma.

Operation: Anchorage
These quests are only available after Operation: Anchorage has been installed. 

The Pitt
These quests are only available after The Pitt has been installed.

Broken Steel
These quests are only available after Broken Steel has been installed.

Point Lookout
These quests are only available after Point Lookout has been installed.

Mothership Zeta
These quests are only available after Mothership Zeta has been installed.