Update: Do not try to remove payment info or visit any Steam Store URLs. You can remove PayPal info, but only do so through PayPal's site, not Steam.
Update #2: The Steam Store servers have apparently been shut down. Also, there is official confirmation from Steam that this isn't a hack.
Update #3: This issue has now been resolved and users can access the Steam Store normally.
Steam is apparently having serious issues on today of all days. Earlier today there was an outage on Steam. According to multiple sources, it appears there is a problem with Steam's caching server, rather than a security breach. People logging into Steam from both the client and the web are seeing the profiles and information of seemingly random users instead of their own. While users seem to be unable to make any changes to others' profiles, this technical issue still puts people's personal information at serious risk. The best thing to do right now seems to be to go offline, as this may prevent more of your info from being cached to Steam's servers.