My kids have the PSP and the Nintendo DS, but by far, the most popular gaming device is their iPod Touch. When they get bored with a game we just download more, for a few bucks, versus $20 to $40 for the other devices. MacMall has the 8GB iPod Touch second generation for $171.98:
Apple iPod touch 8GB (2nd Generation) (MB528LL/A)
Want a better deal?
Amazon has the 3rd Generation 8GB iPod Touch for $181.99, with no tax in most states and free shipping:
They've also got the ones with larger storage, but for the kids the 8GB is fine (unless they plan on putting a lot of video on it).