As email clients are unpredictable, and even today many clients strip styles that are not inlined, it is important to inline your CSS before sending. Don't risk your transactional emails or marketing campaigns falling apart.
We recommend using Juice CSS Inliner to inline your CSS before sending. We use this for our own templates and as it is an open source project it is constantly being working on and improved.
Our email templates come packaged with an inlined version and a non-inlined version so they are ready to go. However once you edit and modify your templates you potentially might have to inline them again. For this we recommend using Juice.
Just paste your HTML in to the input box, see the output being generated, then copy and paste this in to your email service provider.