Yahoo! Auctions is the biggest auction site in Japan, I think (eBay didn't really take off).
http://auctions.yahoo.co.jp/jp/
But, you'll be lucky to find many people willing to ship overseas. Most of the auctions have a "will not ship internationally" notice at the top. You might get lucky and find one that does, but those seem more like the exception from what I've seen.
There are proxy services who will handle the bidding and everything for you, and then ship you what you've won. But add a fee on top (I'm not sure if it's set or a percentage, it might depend on who's doing it), so if you're already buying something that could be expensive like a video game console, you could be in for spending a lot.
There's also Rakuten, but I don't know much about that one personally.
http://auction.rakuten.co.jp/
As for alternative sites (on the lines of video games), these are the only ones I personally know of and have experience buying from:
http://www.play-asia.com/
http://global.yesasia.com/en/index.aspx
http://www.himeyashop.com/
But I think those mainly deal in newer products, although Play-Asia does sell some older things as well (Dreamcast stuff, etc.).