I don’t think too many people need to be reminded that genealogy isn’t free, neither is it cheap. This article comments on the cost of genealogy – perhaps you have a different view? Feel free to share your view in the comments – I’d be glad to read them.
For more visit:
http://hackgenealogy.com/genealogy-free/
Tracing Our History 
The more you delve into genealogy, it is probably not totally free (getting copies of some records, going to places, DNA if you choose that). However, an excellent site that is free and that is improving everyday is Family Search at https://familysearch.org/. Also, Family History Centers at certain local LDS church buildings are also free, have people there to help you for free in your research, and also provide free access to Ancestry.com while you are there at their site. I believe many public libraries in the US also provide free access to Ancestry.com while on their site.
The reason familysearch.org is free is because members of the LDS church volunteer their time indexing census records and other records from all over the world and digitizing other records such as parish records and family Bibles and family histories, also from all over the world. The work of volunteers goes through at least one layer of verification and checking. Some LDS missionaries, often older couples, serve in the Family History Centers I mentioned. All of this (both the web site and the history centers services) is available without proselytizing pressure because they just want you to be able to find your ancestors. They believe it is important and that the Bible talks about the hearts of the children turning to their fathers and their fathers to their children–and this is part of it.
Right now, I like the sourcing capabilities (attaching sources to records) on Ancestry.com better than familysearch.org, but the latter is getting better. Some records I find on one site, some on the other. For the price, though, familysearch.org is a wonderful blessing.
Good luck in your research!
Kate’s genealogical newspaper stories, now from Scotland Neck, NC, in 1880s@Finding Their Stories
and
Kate @ BJJ, Law, and Living