Okay. I'm pretty sure I'm OK on this issue, but I just want to make sure. About a year ago we (my family) registered a domain name for a new website for a nonprofit organization. Tonight I discovered a blog with the same name, but on a blog subdomain. They have been in existence longer than our website. It's not a registered trademark, and it's not registered as a business in our state. So, do I have anything to worry about? I know I haven't provided any real details, but has anyone else been in a situation like this? Thanks

If you want to protect the name, you should register it as a non profit, as well as go after the trade name. Outside of that, unless someone else tries to register the name, you should be fine.

Since they are not a registered business or a registered nonprofit you should have no concerns.
If your concern is "can they take my domain away?"
The answer would be no.

Do you mean like xxxxx.blogger.com and you have registered xxxxx.com? Provided you still own your domain, and you are not infringing on their "in use" trademark rights, you should be ok.

Okay. I think we're safe then. Thanks everyone for the help. :)