Ugh. Where do I start.... Well, i have over 390 apps on my ipod right now, and about 300 more in iTunes.... Here's a simple list from memory of a few apps (all free unless i do ($) after the name).
Oh, and age might be nice. I don't know who to think for, as i have anywhere from kid to adult apps on my iPod so an age would be great to know.
Pocket God ($): You can play god, killing or doing little mini-games with a group of pacific islanders. Very fun, my description is not good.
StarWalk ($): VERY good app, it's astronomy. You can see the night sky/day sky, learn about stars, etc. VERY HIGHLY RECOMMENDED!
Papi Jump: Very fun app, you tilt the device to move a jumper side to side, your goal is to simply get as high as possible without falling.
Gangstar ($): Yeah, it's GTA for the iOS, so age awareness is advised.
Gangstar 2 ($): Yeah, same as above except MUCH more violent/explicit. I do not recommend it for anyone younger than 14 or so.
Pocket Frogs: Breed frogs in this interesting and VERY addictive game. I know quite a few adults who play this
Mr.AahH: Its fun. Should be free.
iChalky ($): hard to describe, kinda like having a voodo doll made out of springs with physics....
ChopChop <insert name here> ($): Three different apps, one of which is chop chop ninja. Best one is ninja, they are VERY fun games.
(company) Donut Games: VERY fun/good games, check them out. Just search "donut games".
Knights Onrush ($): Defend your castle from hordes of cartoon knights, a very solid and nice game.
Crush The castle ($): very fun game, like angry birds, angry birds is actually a rip-off of this.. This game was a flash game on the web, that was extremely popular. Very fun.
Waterslide extreme: slide down 3D waterslides (more fun than it sounds).
Cube Runner: zoom along, avoid cubes, very fun, very free.
Cannon Game: you carefully adjust velocity and angle of a non-line-of-sight cannon to destroy targets. Very clean, no blood/etc..
Catcha Mouse: place traps on a simple 2d game board to try to wall the moving mouse in. VERY highly recommended.
Topple: Great game, build a tower out of blocks.
Tap Tap revenge (2 or 3): Either 2 or 3 is free right now. Both are good. Tap along to the beat in this insanely good game. Also might develop hand-eye coordination along the way.
Paper Toss: Holy c***, what could be more fun than tossing paper into wastebaskets.... A classic.
There you go, thats my recommended apps.... I have a lot more, just those i thought of mentioning. Also look for a app called simple draw, its a simple drawing app. A few other games worth noting are iffy, since i don't know the age/iPod version. Anyway, I hoped i helped!