I've been using the Internet for various genealogy research for about ten years. What you'll find is that the answer to your question is "it depends". It depends on what area, what time frame, what you have to start with, what type of information you'd like to find...
Some states, like Virginia, keep a tight lid on records, not making them public for 50-75 years. Others, like North Carolina, make them public a lot quicker. Some of those records are searchable online, some aren't.
FamilySearch.org, which someone else already mentioned, is a good site and they've added tons of records. Some of the data sets are abstracts and some are digitized copies of the originals. Some are searchable by name, some are not. they have a lot of census records here.
Ancestry.com is a pay site, but they have some stuff for free. Footnote is good for military, especially civil war stuff, its also pay with some free stuff.
The library of Virginia has a good collection of stuff, especially their chancery record collection and the death record indexing project. They also have land grant information, some historical inventory stuff done during the 1930s, etc.
Findagrave.com is intended as a way to search cemeteries, but many people will add some genealogy information to the cemetery record. This one is free.
Check with your public library. A bunch of them will subscribe to genealogy databases and some of them can be used online with just your library card number, like heritagequest. Also, newspaper archives. There are pay sites for newspaper archives, and sometimes your library has it, sometimes the newspaper has some archives online.
And check out books.google.com - searchable online copies of out of copyright books, including old genealogy stuff (books and newsletters). just be sure to check the free books only on the left, or you'll get a bunch with no preview.
And don't forget to talk to your living family. See what stories have been passed down, see who has photos of your family members no longer around, etc. I was visiting my grandmother and asked if she had any old photos. She said no, then paused and thought, then went into the back room and brought out a tintype of my third great grandfather about the time of the civil war.
If you happen to be looking for VA or NC, I may be able to give you some more specific pointers, as that's the area I work with the most.
One last word of caution. Many people put many different things on the Internet. Not all are true. If you care at all about the information being accurate, keep track of your sources. Having a digital copy of a record is much better than some guy said something on a message board in 1995.
Keith
