If you are talking about purely game saves, then something like 80 to 800 (assuming the average game saves are something like 5mb to 50mb. I may have made up these numbers). But there is definitely enough room if you are only using your hard drive for game saves.
But if you are talking about downloading games, XBLA and Indie games vary in size, but at least 3, up to maybe 10, unless you are downloading a lot of really small sized games, in which case you could fit more. DLC also varies in size, but you will likely fill 4GBs up very quickly if you intend to purchase DLC for many of your games. I know I have way more than 4GBs worth of Rock Band DLC on my hard drive alone. And if you want to install or download Xbox 360 games, 4GBs is not enough. Most of my game installs are around 5GBs to 6.6 GBs (I think).
BUT, you can also use USB flash drives to store data.
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