I was wondering if anyone could suggest a site where I could trace my Great Grandmothers ancestry for free. She was from Ireland and she moved to the US in her 20s I beleive.Thanks

Here are a few sites, just to get you started. Some are totally free and some have free trials.
Most will have more links you can go to, too.
The first two also have links to the Social Security Death Index.

http://www.genealogy.com/index_r.html
http://rootsweb.com/
http://geneasearch.com/
http://familyhistory.com/

Also, check with your local library to see what they offer as far as genealogy books, microfilm, etc. We have a genealogy branch to our library, and it is wonderful!