In my experience, flexibility in styles, flexibility on the part that maybe you create (ie from listening or chord chart - the producer/writer may request details such as articulation/tonal/beat placement adjustments...and all those other significants), and the ability to get along with people goes a long way.
I think it depends upon the type of session too - there are those head down and read it types, there are some cool creative sessions where you are called for you input; either way, you are being paid to do the best job you can, efficiently (time vs money...) and to not be a pain!
The way the industry stands, it seems there are less players going from big session to big session so they key in many respects is to say yes to lots of smaller paying gigs that keep you working.
Plus, the internet allows a greater deal of social networking thus people are easier to reach so put your name to them. The flipside of course, is that everyone is doing it!
And, defo ditto the guys above.