If any of your ancestors came to America through Ellis Island, you can check their records for free:
http://www.ellisisland.org/
If you're anywhere near a National Archives office, you can go there for free and access census records and other info for free from that office. Here's a list of the locations:
http://www.archives.gov/locations/
The website has some free info on it, but not searchable census records, for example.
Also, some public libraries have free access to some genealogy websites (that you'd otherwise have to pay for), so check with your local library.