One can't over-state the importance of knowing the PNRs for the airlines you'll be flying, often OLCI (or airport self-service terminals) will work with nothing else. Don't leave home without 'em!

Same goes for ticket numbers, as mentioned above. One time an AA computer glitch left us unticketed on an FCO departure. Everything else about the booking - including seat assignments - seemed so 'complete' I didn't notice until OLCI when the BA computer mentioned a 'slight irregularity that will require airport check-in'. "Fortunately" the glitch dated the booking a year later which thwarted the normal ticketing progression but left the reservation on perma-hold until the humans straightened it out. Good thing we were uncharacteristically early for the flight.