I've used compression for as long as I can remember - I had a little half-rack Boss compressor when I was in high school, though I'm not sure I really knew what I was doing with it or how good it sounded - I also had a crappy amp so I was probably trying to protect the amp.
For the past 10-15 years, I've been using a tube compressor from Custom Audio Engineering/Custom Audio Japan:

I'm basically using it to help me gauge my right hand (whether pick or fingers) - I have always had a tendency to play too hard - and also to get an idea of the various volume outputs of my basses - I use it with my Stanley Clarke, my Activator equipped P-Bass, my stock Duck Dunn P-Bass, my Gibson Les Paul - they all have different volume outputs, so the compressor helps me a lot.
One important thing - I can't stand compressors that don't give a visual indicator of when the compression is hitting.