Happy Birthday to You

 is an unmarked Fallout 3 quest.

Little Lamplight
Once given clearance to enter Little Lamplight by Mayor MacCready, the gate opens to display several child NPCs gathered around a teenaged NPC wearing a red birthday hat.

Sticky has just turned 18 (he mentions that all who turned 18 must leave during one of the dialogues) - and at this age, it's time for him to leave the Little Lamplight. When you speak to him he tells you he wants to go to Big Town, where all the grownups go.

Escort
Once Sticky joins your party, you may give him weapons and/or armor (even power armor) which he will then use to defend himself.

During the trip, Sticky talks quite a bit, sometimes making up stories presumably chosen at random. His stories follow a Mad-Lib template; similar stories repeat, with only about half the words changed. You can choose to put up with it, you can tell him to shut up, or you can kill him with impunity (no Karma loss).

This quest is completed once crossing the bridge to enter Big Town.

Bugs
The quest will sometimes complete itself if he gets too close to the edges of big town's walls on the outside; rather than once you have him cross the bridge.