I have seen lots of complaints about EVE server problems in EVE Reddit and here at EVE general discussion area. Recently there has been complaints about login server problems. Then there has been complaints about Jita local been down and chat server problems. Earlier weeks there were complaints that traffic to EVE servers was blocked from countless IP addresses. They were probably somekind of anti-DDOS measures.
These links here were just few examples of long line of complaints from countless people.
edit:
Lots of people have also made complaint that they lost their ship in abyssal space because connection was lost all of sudden.