I think you did the best thing by logging out of your Google account, and now doing that every time. What's to stop anyone from getting in - such as a spambot? Those things are programmed to look for gaps like that...sneaky little ninjas that they are!

I only got spammed once on Facebook - by the second of my two accounts. Only on the internet can you spam yourself... On FB I make sure I change my passwords on a regular basis...Gmail too.