At the risk of looking waaaaay too indulgent (and I’m not even a parent yet):
DJ Baby is a simple iPhone/iPod Touch app that lets even small children rock the turntables. It’s dead simple to use: Each of the four “records” has a vocal sample, and the button with the musical note starts and stops the backbeat. Clicking on the needle varies the vocal sample a little. You can try out the app online (Flash required), although it’s more engaging with the touchscreen interface. Plus, if you shake the device, there’s a bonus sound effect!
The app is definitely easy to use: Basically, if you trust your kid to hold the device, then they’ll be able to figure out the interface. And the target audience–say, 6 and under?–will almost certainly find it diverting, although children in the older part of that range might not be willing to play long at a stretch without asking to play something else.
The simplicity has some consequences: there’s no way to save a beat, nor is there a way to create your own sample, whether by recording your voice or using a track from iTunes. You can see why: It would defeat the whole purpose of the app if you were constantly being called over to fiddle with settings.