It started out innocuously. We were waiting for a table at a restaurant, my daughter was about two years old and fidgeting. I checked the App Store on my iPhone for a kid genre, found a fake phone game, and let her go to town on it. It saved the day and bought us 20 min of quiet time. Since then I've downloaded a lot of games and educational apps for my daughter (who is now four and a half) and I've been meaning to write up the ones I think are worth a few bucks and have stood the test of time, and here they are.
This is my "Kid Games" screen of my iPhone that I go to when I find myself somewhere with my daughter and we're both bored. This happens sporadically in doctors offices, in lines while running errands, and most often at a restaurant. I'll quickly recap each one here with an appropriate age range after.
Fairy Trails — Augmented Reality for Kids! If you have a newer iPhone 3GS, this is a game that initializes the camera and you pan around the room, clicking the screen when you see a fairy fly by. It's pretty simple and kind of silly but can entertain kids for longer than you think (3-5 years).
Brushes — fairly advanced drawing tools than can trip up younger users (by them accidentally zooming out or in), but for general drawing works pretty good (3-12+ years).
iPlayPhone — the first kid game I downloaded. Mostly just a noisemaker for the youngest to mash on without messing up your phone (6mo-2 years)
Ballonimals — Pretty fun virtual ballon animal game from IDEO. You blow in the mic to make an animal, tap it to make it dance, then explode it by over-inflating. Good fun (2-6 years)
DinoMixer — It's a mix and match game of dinosaurs, with about a dozen different animals in three parts plus different foregrounds and backgrounds. Fun and a good learning experience (3-10 years)
TicTacToe — there are about 100 different TicTacToe apps in the App Store but this one allows for WiFi play, which I've done with my daughter using another iPod Touch. Good times (3-10 years)
ZenGarden — a really great simple "drawing" app where there is no color or brushes to choose from, you just push a line in the sand, and shake for a new blank canvas. Perfect for young artists (1-4 years)
Heat Pad — much the same as ZenGarden, you just drag a finger across and colors change, this one is a fake "heat map" based on how long your finger stays in place. Gets old kind of quick, I've found (1-4 years)
Cute Math — A nice basic number identification, counting, and eventually basic addition/subtraction app. (2-6 years)
LunchBox/WhenIGrowUp — Both THUP games come from a developer that is a member of MetaFilter where I heard of them. Great pre-school games, one is basic number and color identifier, the other is basically dressing up a monkey. My daughter loves both. (2-6 years)
AnimalMatch — My daughter loves Memory card-matching games and this one offers flexible grids of different sizes/difficulty. There was a time she wanted to play this for hours (2-6 years)
Let's Color — A Curious George/PBS app, this is just a paint-bucket coloring book style app. If your child is a fan of the show, they will like it (2-4 years)
DoodleBuddy — Amazing drawing app that is free(!) in the App Store, and is perfectly between something full-featured like Brushes and simpler apps. It even offers collaborate WiFi drawing between iPhones/iPods as well. It's worth $5 even though the basic version is free (3-10 years)
Pickin Time — Fun simple reaction-time game where you click on fruits/veggies as fast as you can. Works well when competing among several people to see who gets the highest score but game gets old quick (3-10+ years)
I've tried dozens more and deleted them all when my daughter grew out of them or no longer found them interesting. These have stood the test of time and lasted several months to several years, and most are just a buck or so.
Though I wouldn't suggest using these to ignore your kid or thinking that you just have to have them around all the time (crayons and paper are usually a bigger hit than an iPhone) these apps have come in handy when there's been dead time to fill and nothing to play with.