I always enjoy trying to beat a shooting game's campaign without ever firing a weapon. Most often I will try to only use melee, but other times I will use grenades as well. On easy, this method of play is completely possible but the higher difficulties require some real skill. (I do make exceptions when gameplay requires it, such as in vehicle/turret scenes where there is no real alternative)
The one game that comes to mind is Medal of Honor: Rising Sun. It is a pretty shitty game but when playing with a friend, only using melee is a lot of fun. The enemies just stand there and take it while you take out entire platoons (only loosing half your health in the process). Another memorable game for this method of play was the first Halo.
For Battlefield 1942 online play, I would sometimes only use vehicles to hit other players or get them with car bombs. Hitting players on the ground in a plane took some real skill, but it always pissed of the victim. Also, tying to land a plane at ridiculous locations, on top of the enemy hanger or on enemy battleship, or using the planes as ground assault vehicles was always very entertaining.