This is going to depend on how much you are looking to spend. My 5 year old has a VTech MobiGo 2. He really likes it. Very durable, age appropriate games, comes with a stylus, but you don't have to use the stylus (figures work, too, on a touch screen). The only down side for me is that the games are all cartridges, so it's easy for him to drop them in the couch cushions or something. He doesn't always know where the games are.
My 8 year old has a IPod Touch (4th Generation) that his grandma bought off Craigslist for about $100 or $150. The newest versions start at $200, I believe. There are so many apps you can download. Many of them are free. The nice things about apps is that you can't lose them.
I think a tablet might be more appropriate for a 6 year old. You might be able to find one on Craigslist for less than $200. You can also buy a case for it so that it's protected. The advantage really is that there are no games to lose. Cartridges for the VTech, Leapfrog and DS are all so small and very easy to lose.