We have more gaming systems in my house than you could guess. My husband and I both play and we have a Wii, an Xbox 360, a PS2 (older system), a DS, and two DS Xls. I wouldn't recommend the DS for a "family" system because the screen is small and it's a one person game. (Unless you have more than one and then you can link them.) The PS2 is a good game system and has tons of cheap kids games available, but it's already one generation from being "new."
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It depends on what kind of games you like and what type of controller you like. The Wii and Xbox 360 are both excellent systems.  (So is the PS3, but it's newer and has fewer titles available.) The Wii has a motion-controller and nun-chunk that is a bit harder to use for my kids. On the other hand, there are lots of family titles for the Wii that make use of that motion-controller and my boys really like them. They also really like the Super Mario titles for that system and that controller. The Wii is a newer system so it has fewer titles available, but still has plenty to choose from.
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The Xbox 360 is a bit older and uses a traditional "button-masher" controller. The controller is easy to learn. There are more titles for this system, but probably not as many "family" titles. It's probably going to be an obsolete system before the Wii. I love this system, though. It's my preferred platform for ease of use.
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In either choice, I highly recommend the Lego Star Wars games for a 7 year old. They're very fun and not scary at all. We had a good time with Mini-Ninjas, too. I found "Mario and Sonic Go to the Olympics" series to be too hard for kids and boring for adults, but "Super Mario Galaxy" and "Super Mario Galaxy 2" were right up their alley. (But they make me dizzy to look at.)  We had high hopes for "Endless Ocean" for the Wii, but it was pretty boring. My kids really enjoyed the free sports games (bowling, baseball, golf) that game with our Wii.