So you're getting a security error when picking up other email accounts in Gmail like this:
Server returned error "SSL error: self signed certificate"
What does this point to? Well it seems that on 12th December 2012, Google decided to update the way they fetch external emails within Gmail and now insist on the server having not just a self-signed certificate but a full-blown one. That's OK, but it would have been nice to have been told about it.
Full certificates can cost an arm and a leg (lots of money!) and they are quite varied in features. I am a big fan however of the Rapid SSL Wildcard certificate from the SSL store which fits the bill and is very keenly priced. This currently has a huge $78 off and can be used on your whole domain, ideal if you have multiple domains or even just want to do Facebook timeline stuff later on (this requires SSL certification too). If your website has a shop on there, I would heartily recommend the Comodo Premium SSL Wildcard Certificate from the same guys which I have used on a few VPS and dedicated servers.
If you just want to get up and running quickly for free, you can simply drop any SSL external accounts to port 110 (POP) and port 25 (SMTP) which should get you live again. Send a few test emails to check things are running OK. Bear in mind that this is then transmitting emails insecurely so the domain will need the SSL certificate as soon as possible. While the Rapid Wildcard Certificate mentioned above is on offer it makes sense to lock things down sooner rather than later.
Please drop me a comment below if you get chance and this helped you out!