Edit: Everything is apparently fixed now. What actually happened is still a confusing mess of caching.
Something is very wrong with Steam today. After Steam went down from too much traffic, people started realising that they were no longer logged in as themselves. This was most obvious when clicking on one’s Account Details, you’d see the information of, well, not you, the most revealing of which is payment information, Steam Guard details, your shopping cart, your purchase history and your email address. Don’t panic just yet.
What can you do as of now? No one’s quite sure and Valve has currently turned or is turning everything off. But first off, DON’T PANIC. That only makes things worse.
Your best bet is to stay away from all Steam-related websites, ESPECIALLY the store. You can’t currently unlink any payment information, so don’t do that, as you may end up revealing more information rather than removing it. Keep an eye on your email and mobile verification, as you may get alerted to any unusual activity via there.
If you want to unlink something, ONLY unlink it via Paypal or your bank, do not do anything via Steam. Do not use the Steam Store, and avoid as much of Steam as possible. If you see someone else’s information, do them a favour and don’t touch any of it, and try to ignore it. For the love of the Bahrag don’t share it with anyone.
Steam Database (who aren’t affiliated but seem to be the only people with any decent info on this) on Twitter has some useful information on what’s going on, as well as a blog post summarizing it all. SPUF is up and down, so you probably won’t get any information there. There’s information on Reddit too.
If there’s any more information, I’ll do my best to update it here.