http://www.county-clerks.com/ - Thanks to Raymond Zaroder, who developed and continues to develop this website and alerted me to it. He was researching his own family history when he realized there wasn't a a good database for getting court records.
http://www.ancestry.com/ - I discovered a lot about my family using this tool, and it also put me in touch with some long-lost relatives! There is a fee to use it, but trial memberships and special offers abound.
http://www.usa.gov/Citizen/Topics/History-Family.shtml - This takes you to numerous other links, such as genealogical and historical associations by state, military history, immigration records, and much more.
usgenweb.org/ - Free genealogy and family history source. The home page takes you to links according to states. I tried out my county in Tennessee and saw a note from someone offering to help others do lookups. Nice:)
http://www.grundycountyhistory.org/ - Local history sites can be real treasures. This one was found through a link with the Grundy County Historical Society and not only contains written family histories, but oral histories on video! Some towns, such as Walnut Creek, California, even have their own web sites that include individual and family histories, both written and on video. (See what I mean at http://walnutcreekhistory.info/
http://www.findmypast.com/content/20-family-history-resources - This site lists some of those already found in the other sites, but also provides ideas for finding information within your home and family, in newspapers, churches, and more. It also a discussion about oral history and podcasts
https://familysearch.org/family-trees - This is a huge database sponsored by The Church of Jesus Christ of Latter-Day Saints and is free.
https://www.facebook.com - I'm not suggesting Facebook as a major resource, but if you already have a living relative's name and location, it might put you in touch. It's worked for me! You might be surprised at how willing and eager relatives can be to assist with your search. I'll bet you can name at least two or three people in your family who have already done some research. Hey, that's another great starting point, right?
https://www.google.com - Just google it or use another search engine, if you have a preference. Type in a family name and you might be surprised what pops up. There are whole websites developed to particular families. I don't have many famous ancestors, but I still found bits and pieces of information. My husband does come from a family of writers and scholars, and I found volumes of information oh his heritage!
Have fun, and good luck!