I own several domain names, some for over a decade. A few years ago I moved them all to a Virtual Private Server, and all was well. A few months ago I had to move to a different VPS provider, which necessitated a new mail server, which I had to manage myself. It's now more than I can handle, and I want to move my email hosting entirely off my VPS and onto an e-mail provider, but leave my websites on my VPS. My domain registrar is different from my VPS provider (which I've heard is a good idea), so I'm looking at dealing with at least three different providers.
What do I need to know to avoid shooting myself in the foot, domain-wise? I'm a programmer, but not a sysadmin; I know just enough about DNS records to be dangerous.
All you'll need to do is choose a new provider, get their service set up to accept mail for all your domains, and then create (or change) MX records for all your domains to point to the IP address of the new service's SMTP handler. They should be able to tell you the IP address when you sign up for their services.