There is a mass of genealogical material on the web. The sites below are just the tip of the iceberg: please let me know of any others which you think I might add to the list!
A good place to start your researches is one of the big sites like RootsWeb. It holds vast numbers of records – mostly deposited by other researchers, and varying somewhat in their accuracy. It also has message boards, where you can find forums (fora?) devoted to almost every surname imaginable. I’ve found out a lot by exchanging knowledge with fellow researchers in this way, especially on another set of message-boards, GenForum.
The Mormons have the strange habit of converting the dead (so much easier for them, and relaxing for the rest of us, than targeting the living). So they put enormous energy into collecting records of our ancestors, and the fruits of their labours are in the International Genealogical Index. This holds a vast array of baptism and marriage information from around the world, as well as a growing number of family-trees deposited by individuals. (I find the accuracy of these more than usually unreliable – perhaps because of contributors’ zeal to get their forebears into mormon-heaven, which leads them to get someone else’s great-granny there instead.)
Births, marriages and deaths in Great Britain have been subject to civil registration since 1837, and there’s a project, run by volunteers, to index these digitally. The results are at FreeBMD, a resource which is growing rapidly and which the organizers anticipate being complete in 2007. Ordering certificates from abroad can present problems, but a small-scale site, Certificates, offers to do so quite cheaply and apparently accepts credit card or foreign currency cheques.
Additionally, the 1901 Census is now on-line – though you need to pay to see more than the index. For British records generally, GenUKI is a “virtual reference library” which holds some fascinating details of people and places.