The DS is a great handheld gaming systems. Your kids can throw these things on the floor and they'll still work. The only thing that seems to stop these things is water. You want to keep them far away from water. We've had two gameboys that died because someone left them on the counter and a drink spilled on them. Other than that I don't think you can break them without really trying to break them.
A question I get from time to time is "Is the DS better than the PSP?"

This is not a simple yes/no question. I feel the DS is suited for a more passive audience. That's usually why I suggest it over the PSP for kids. For parents there are a lot of games like Mario and Transformers that will keep them happy, but overall the DS isn't the system you'd find games like Grand Theft Auto on. Another reason to choose the DS over the PSP is due to the fact that it is a cartridge (memory card) type system. There are no discs to scratch or disc caddy's to break. The PSP has a big problem in that the disc caddy's break after a few months of careless use.

It used to be that with the DS you could play both DS games and Gameboy Advance games, but with the new models such as DSi and the DSi XLthat doesn't work anymore.  If you can find an older DS they work with both types of games which can save you a bit of money.  There are many used Gameboy Advanced Games out in the stores like Funcoland and Game Stop. The prices vary, but I'd bet you can find a few for $7.99 or so.

If you want to buy a portable to play movies then I'd go with a PSP or Apple iTouch. The PSP screen is great when playing movies. IRobot looks great on the wide screen. Also, you can get a lot of PG-13 and R movies for the PSP so if you're looking to take your movies with you, then the DS is not your option. Hope this little bit of info helps in your search for the right portable game system.