How literally should we take the question? I’d be tempted to list the SDMB, but if everyone can only use three websites, this place would be a ghost town and there’d be no point. Ditto facebook, ditto youtube, ditto a whole host of file-sharing sites, etc.
So, I’m going to interpret the question to mean that I can only use three sites. In that case:
Wikipedia (I need the internet to be a source of instant info.)
SDMB (I need the internet to be an opportunity to socialize.)
Amazon (I need the internet to be an opportunity for commerce.)
Just missed the cut: espn.com, nytimes.com, The Onion, youtube, eBay, twoplustwo.com (poker message board)