What is a good gift for a 13-year-old girl's birthday?

Jesus

no but seriously, Video Games?

Depending upon the console he has:

Xbox Originial

Halo 1, Star Wars Knights of the Old Republic 1, Fable, Ninja Gaiden Black, Doom 3

Xbox 360

Gears of War 1 or 2, Halo 3, Modern Warfare 2, Viva Pinata, Burnout Revenge, Rock Band (if he has friends), Grand Theft Auto 4, Red Faction Guerilla, Saints Row 2, Assassins Creed 3, Halo 4, Saints Row the 3rd

PS3

Lair, Killzone 2, Drake's Fortune 2, Little Big Planet, Batman Arkham Asylum, Assassin's Creed 2, Assassins Creed 3

PC

Dragonage Origins, Left 4 Dead 2, Borderlands, Dawn of War: Dark Crusade, StarCraft (old but without a doubt one of the best games made), Team Fortress 2

If he doesn't play videogames, then I don't really know what keeps 13 year olds entertained. Money is a cheap cough out, but it works :/

Another person: or if you are talking about a girl you can give her a kiss :) It will keep her happy, or a boy, the same thing would help.

Anyways you can take He/she on a date, or something, you can ask him/she yourself what he/she would want for christmas. (It might not make it a surprise but you need to know that he/she would be entertained for a few yrs. depending on what heshe asked for