Litmus and Email on Acid are undoubtedly the big players in this field, but here’s my personal cheatsheet for getting started with email testing:
Mailchimp has a built-in email testing offering, powered by Litmus:
… but you can only do so many tests per month, it’s basically a shareware version of Litmus I guess.
Campaign Monitor has their own offering, which is free if you’re on an Unlimited or Premier plan:
When testing emails (which is not very often), I also like to review Mailchimp’s email design docs to find bad practices I should be looking out for, and better practices that I could suggest in their place:
There’s also this free standalone tool, now owned by Litmus:
It doesn’t show you what your email will look like in different clients, but if you want to take the DIY approach then this tool will do the complicated bit (sending the email) for you.