When I travel revenue (which is almost always now), I am a meticulous planner. The day of the trip I print out at least 3 alternate routings, I have all the airlines on speed dial, and am prepared for anything!

I've been lucky though, and have never missed a connection in my relatively few flights.

Another thing that helps is knowing coworkers for other airlines...if I have issues, I give a friend a call at that airline, and they do what they can for me.