Designing for web browsers is easier now than in past years because more browsers are following standards…for the most part. There will always be problems with Internet Explorer because Microsoft seems to incapable of debugging but it is better than it once was.
Just like browsers, many email browsers work similarly, except Outlook and Outlook.com, but you do have to pay special attention to how you design your email code. If you ever wondered why so many companies send emails that are just a couple of images, this is why. It’s easier to send an image than format text but you have more risks with spam filters and low open rates because people can’t see the image until they click the “show images” button.
If you want to get an idea of the differences in compatibility, take a look at this chart. I use this for most emails I build to make sure they are as compatible as possible. You can download the full chart or see the top 10 email clients right on the page.