So far, Groupy seems to be working pretty well for me. Two things that come to mind that I would like to see supported are:

• The ability to add new window using CTRL+T similar to web browsers, Linux, and OSX. I would imagine this feature only being made available if the Only group windows of the same application or type with each other setting was enabled. Adding a [+] button to the right of the tabs would be nice as well. 
• The ability to close an entire group. Having both a keyboard short-cut (i.e. CTRL+ALT+F4) and a button on the group's title bar would be helpful.

I could also see bullet #1 above working even without that one setting enabled. Basically, if the active window/app currently supports CTRL+N, I could see CTRL+T launching a new instance of that window/app as a separate tab. If the window/app does not support CTRL+N, then CTRL+T could just be totally ignored.

Sorry if these suggestions have already been made. If so, consider this a +1 for the other person's suggestion(s).

Overall, I do like the simplicity of Groupy so far and can totally see it's potential.  Keep up the good work.