Currently, minecraft.net is down. When minecraft.net is down you can still play single player, but multiplayer won't work. You can connect to a server, but login will fail with a 503 errror.
To temporarily fix the problem in v1.3, edit the server.properties file stored in the same directory as the server jar/exe. Change online-mode=true to online-mode=false to disable account authorization. Save the file. Restart the server and you'll be able to connect without a 503 error.
Warning: This fix should only be used temporarily. Since authorization is disabled anyone can login as any account. As soon as minecraft.net is back, re-enable authorization.
Players with the new game launcher will have their correct usernames and items. Players with the old launcher will be named "Player" and not have their items. If only one user has the old launcher, it is possible to rename their user data to "Player" and allow them access to their things. Change it back once minecraft.net is up.