[First posted 09-Mar-2010 here]
If you care about your privacy and identity then be sure to read and vote on this JIRA issue
In short, any Shared Media prim has the potential to get all sorts of information about you – IP Address, Operating System & version, language (gives a good idea of country), Client & version, all sorts.
Possible exploits are linking alts to mains, griefing, stalking, RL harassment, phishing, malware and viruses.
The JIRA entry and the subsequent comments have a lot more information. And this blog is also worth reading.
I’m kind of surprised how few people seem bothered by this.
Update: This blog comment highlights a very scarily plausible scenario for how a phishing attack could successfully compromise your SL account.