After the problems that happened on 10/11/12 (minecraft.net was down, logging in was unavailable, skin service was temporarily unavailable) there has been an issue regarding connecting to servers. I have only seen this happen if they have online-mode=true, so far. The player will try to connect, and it simply tells them "Error: Failed to log in" or it will tell them that they took to long to log in, as well as the occasional "End of Stream" or "Java exception" errors". It will often take up to 5 tries to connect to a server.