The only "free" services that I can think of would be to search your last name- all of them. You can always try googling the names of some older family members, or going through family albums (though that's not online) From your last name you should be able to get at least where you originated from and a few more well-know/famous members of your family.

I have this problem too, I only know half of my roots, and I don't think I should have to pay to know the other half. Good luck to you.

Try FamilySearch.org. Completely free to sign up. It can be a somewhat hit and miss - some of my ancestors show up, some don't. If you manage to find an ancestor who would have been alive in 1881 (I am assuming English/Welsh descent now), you can access 1881 Census records for free.

You can also visit your library - a great many public libraries (certainly in the UK) now have a corporate membership for Ancestry - you can't save a tree to the site, but you can do your research and make notes, then transfer to your own program at home (RootsMagic have a free downloadable program).