There are now many genealogical sites on the web so this list is by no means exhaustive. These are links to a few popular locations.

Huge databases for many countries. Subscription needed to access most information.

Excellent data for English & Welsh births, marriages & deaths from September 1837 to early 1900's. Free site.

Comprehensive mainly American & British data pre 1900. Mostly births and marriages. Free site.

Everybody should start here. A good guide to records. Free site

I think this is the best genealogy software in the market and it's FREE.

Popular UK site. Offers a limited free membership but subscription needed to access most information.