HTML formatted email not showing up at all in Gmail but is in other mail clients

I am updating my answer since it has quite a few views, and new tools are available. I am leaving my original answer for posterity.

Edit * 9/19/19

You can find CSS property support by email client here:
https://www.caniemail.com/

Original Answer:

Gmail does not support the <style> tag. You need to use inline css for gmail to work correctly.

Here’s a reference list.
http://www.campaignmonitor.com/css/