Up first, is the classic comm, the silver arrow on the gold background. I have included a picture.
My second badge was actually in the episodes 'Future Imperfect' and 'Yesterdays Enterprise'. It was worn by Marina Sirtis who played Diana Troi. I have included some pictures for reference. You will note that one of the bands have broken off while in storage, and the colours of the bands depict a rank of 'Lieutenant Commander' It also has 'Troi' written on some tape attached to the back of the badge.
My last badge is in the Style seen in Star Trek: Generations, and also throughout Voyager. It is marked X2 on the back. I believe this was used in Nemesis, but cant confirm it. I came to this conclusion based on a Charity Auction a couple of years ago. At the time there were 4? badges for sale, with the same code format being used. It was stated from the seller of the items that they came from Star Trek: Nemesis. I believe the 'X' Denotes 10, as in the Roman numeral, and 10 being the 10th movie IE Nemesis. As I said, I cant confirm this, but makes sense in my mind!