One of the great things about this game are the companions. Sure, they may have their bugs, but they were done really well. However, I have two suggestions that I believe would make companions more useful or interesting to a variety of players.
1: Let us do flashpoints with us and three of our companions.
Flashpoints are great and all, but I don't like having to go through the hassle of finding a group to do them, especially considering I play at odd hours on a light server. I know server transfers/merges/etc. will be here eventually, but I would much prefer to do flashpoints with my companions, as I have worked hard to gear them all up well, because that's something I enjoyed doing.
2. Let us put companions in our Legacy family tree.
This feature is something role players, and many other players, would enjoy. As simple as the family tree is, I love it. Companions all play a large part of our story and I think they deserve to be a part of our legacy.
Here is an example: I am a trooper who is a Zabrak and I married Elara Dorne, a human. Most of my other characters are also Zabrak or Human, so I have a nice tree right now. However, all of my characters are men, so my tree is still lacking. Elara and I at the top of the tree would just make everything look so perfect.