From my experience they want to see the usual aircraft and crew documentation, like registration, radio station licence, sometimes the AFM, insurance coverage, crew licences (radio operators licence too if its not integrated in the licence), logbooks (journeylog/aircraft hours, technical log, crew logbooks) and all documentation for that flight, like weatherbriefing package, NOTAM package, operational flightplan including the usual notations (one fuel check per hour of flight) and of course a load sheet (weight and balance).
I might have missed some since its been a while. For the flight log/operational flight plan i got once quite a speech about crew responsibility from a french CAA guy because we had only done one fuel check on an one hour twenty minute flight instead of two.
I'm sure someone will probably dig out the relevant CAA/EU-OPS rules about ramp checks
