Vault-Tec Bobblehead

The Vault Boy bobblehead figures were promotional Vault-Tec items.

Each of the Vault Boy Bobbleheads in Fallout 3 permanently increases one of the 7 statistics (S.P.E.C.I.A.L.) by one point or one of the 13 skills of the Player Character by ten points.

The bobbleheads will not increase a statistic beyond the maximum of 10 (S.P.E.C.I.A.L.) or 100 (skills).

Players can store the bobbleheads they have found in their house in Megaton or in their Tenpenny Tower Suite. Two of the Fallout 3 achievements involve collecting Vault Boy Bobbleheads. The first achievement is awarded for collecting 10 of them, and players earn the second for finding all 20 of them.

More Guide
Look at Yes, I Play with Dolls for a more detailed guide with pictures!

Stats
These increase the listed S.P.E.C.I.A.L stat by 1 point (to the maximum of 10).

Side note for cheating in the PC version: In order to gain any stat raises from a bobble head they must be picked up from the game world, rather than added to your inventory. To get the stat increase without finding the bobble head, it is recommended that you zoom out, go into the console, click yourself, then type "placeatme [objectid of desired bobblehead]" in the console. This should spawn the bobble head at your feet where you can easily pick it up and get the stats.

Additionally, consider the player.forceav Console command, which will let you set your skills and attributes to whatever you like.

Skills
These increase the listed skill by 10 points (to the maximum of 100).

Behind the scenes
The bobbleheads were also used as a Fallout 3 promotional item by Bethesda Softworks and are included in the Collector's Edition of the game. They are identical to the ones in-game, but have arms crossed in front.

See: Fallout 3 promotional items.