Okay, the support of my hoster wrote it's probably outdated software or a virus.
Well, I'm just confused. My two Windows 8 computers are always up to date with everything, Windows Defender is running. I use the Windows 8 mail program and Outlook 2013 in addition. I don't think that's outdated. Also, I don't visit porn, illegal download or other shady pages. I also don't install software I don't know or trust. In addition I have configured this email address on my iPad and on Windows Phone. I think those are devices that don't have viruses. I don't check this email account on the Android phone.
Sometimes I visit the web interface of the mail address from my work computer, I don't think that one has a virus either.
What is true, the password wasn't too bad, but I haven't changed it in ages. Could that be it?
Well, I have changed all the passwords now and I'll check my computers for viruses then...