With the exception of the Akilians, I tend to leave them alone. The Akilians have an annoying tendency to drop influence bases next to my homeworld, for which the punishment is DEATH. I'm going to be editing them out of the XML file soon anyway.
The other ones... I like trading with them. They usually have pretty good economies, they usually have pretty good tech to trade for and I can go to war with the major races without losing a trading route (or three).
On the other hand, especially later in the game, the major races react almost instantly to a newly discovered minor race with an invasion. It makes me sick, so I usually end up giving them a fleet of warships and any military tech they don't have already. Most of them can't make use of the warships for some reason, but the other races don't seem to realize that, so they impale themselves on the warships that are just sitting there. If they at least have the brains to park the ships in orbit, I'll build them a military base with all the ship assist stuff. Makes them nearly impossible to invade.
Some of the minor races can become as powerful as the major races. They'll send out fleets of warships, invade planets, etc.