I love the idea of ancestry.com, but I can't pay for anything like that right now. Are there any similar sites that I can access for free?

The simple answer is no. There is no "free" site that has the kind of data available on line that these sites have. But... much of the data is available free if you take the time to do the research, but much of it is not available directly online.

Check with the reference desk at your public library. Your library card may give you free access into various ancestry databases that the library subscribes to.