NEW v3.1 Field Groups
I don't know if you want just one thread for all things "Field Groups" or separate threads. Either way, I've given it a quick go and have an observation/question:
Using a Field Group around 'standard' fieldtypes works exactly as you described. However, I also tried using a Group around some custom fieldtypes and the Group UI ignored the custom fieldtypes, instead wrapping itself around the first available standard fieldtype above the custom fieldtypes.
If for the moment it only works around standard fieldtypes, that's fine.
A very small thing with the UI - I can't click on the rotating arrow/circle image to collapse the Group. Clicking the title text bar (expanded) or the body (collapsed) works fine - my first instinct was to try clicking the (small) image! This was on Chrome version new-ish-something-or-other.