"We're aware of a problem with Google Mail affecting a majority of users. The affected users are unable to access Google Mail," mentions Google's Apps Status page. The message was posted at 0:53 pm PDT and Google promises to solve the problem in less than an hour.
Gmail's web interface can't be accessed, but you can read your messages and compose mail if you use Gmail's iGoogle gadget. Another way to connect to Gmail is using a mail client like Outlook or Mozilla Thunderbird: POP3 and IMAP come to the rescue.
Update: Gmail is back up, after more than one hour of errors and timeouts.
Update 2: Ben Treynor explains why Gmail was down for 100 minutes. "This morning (Pacific Time) we took a small fraction of Gmail's servers offline to perform routine upgrades. (...) However, as we now know, we had slightly underestimated the load which some recent changes (ironically, some designed to improve service availability) placed on the request routers — servers which direct web queries to the appropriate Gmail server for response. At about 12:30 pm Pacific a few of the request routers became overloaded and in effect told the rest of the system "stop sending us traffic, we're too slow!". This transferred the load onto the remaining request routers, causing a few more of them to also become overloaded, and within minutes nearly all of the request routers were overloaded."