Safe to put art on Facebook?

I have always been afraid to show off my artwork on Facebook or Tumblr. Couldn't someone just steal it & sell it or put it in their own portfolio pretending its theirs? Couldn't it be ped around the internet under someone elses name then, and discredit me as the creator of my work? Are any of my rights protected if I post my art on Facebook or a blog (tumblr)?