As a surgical resident I avoid the following cases if I can scrub a different one instead.
1) Where the attending is in over their head. This is rare, but I don't want to be named in the inevitable lawsuit.
2) Where there are fellows or senior residents scrubbed in ahead of me. I won't get to operate.
3) Routine boring cases, especially if a more interesting one is going on next door.
4) Cases where I will retract the entire time and not be able to see what is going on (standing on the opposite side of a pelvis case retracting).
5) Where the attending is overly handsy or is a jerk, both of which will lead to an unpleasant operating experience.
Truthfully though I pretty much go where I'm told. Rare to get the option which case to scrub.