Before I owned a digital camera I would take my 35mm film camera everywhere I went. One concern I always had was whether or not my film would be ruined going through airport security checkpoints.
With traditional film cameras, there's a higher risk that film will be damaged by the X-Ray machines during security screening, even though this hasn't happened to me. Just to be on the safe side, have your camera checked separately by hand or ask the security staff if the X-Ray machines are safe for film - usually the posters in the area will indicate whether or not you need to remove film. As for digital cameras, your pictures should be completely safe.