An interesting twist on the "stake cut" suggested by Jefro is to suspend the 2x4 horizontally (from an eyehook or whatever at each end) - gets to swinging when it is being hit, and can also 'bind up' when it starts to break - quite a challenge. (We used to use 4x4s or the like, with somewhat larger teams.)
Another very popular event we used to hold was a "Wounded Man" shoot - two man teams, each with their weak hand/arm immobilized by tying it off to their belt in back. Between them they have to load and fire a muzzle loading rifle as many times as they could in a certain timespan (e.g. 10 minutes.) Requires great co-operation .... holding the rifle between them, each one being designated to perform part of the loading procedure: e.g. they could settle on something like this .... 'A' holds the powder measure while 'B' fills it, then 'A' dumps the powder in and drops the measure to the end of its thong while he retrieves a spit patch from his mouth and places it over the muzzle; meantime 'B' is fetches a ball and centers it on the patch, while 'A' positions a short starter on it and presses it down, then 'B' whacks the short starter to get the ball started; 'A' retrieves the ramrod and they ram the ball home. Then the shorter of the two (usually) grasps the rifle by the forestock and swings it up onto his shoulder and holds it there as steadily as possible, pointed at their target, while the other fetches a cap and caps the piece, then aims and fires the rifle using his partner as a support. Repeat as time permits, and the best scoring target wins. This can be a real hoot if all teams are shooting at the same time, but also presents much greater possibility of accident. A safer way, if time permits, is to have each two-man team shoot by themselves - much more entertaining for everyone else to watch .... and all act as "safety officers" .....
Another good one is a "Beer Can Buddy" event. Each two man team has two beer (or soda) cans set out at a reasonable distance, one filled with water and the other empty and balanced on top of the first. One member of the team has a loaded rifle and the other a shotgun. First shooter shoots the bottom can with the rifle ..... if he hits it right, the water pressure launches the top can into the air, and it must be hit by the shotgunner (i.e. at least one - or more, your choice - pellet holes must be found in it for the team to stay in the running. Process of elimination until a winning team prevails. (The 'wild card' in this one is that the top can may take off horizontally or at some other strange angle .... or not go anywhere at all.)
"Partridge Picking" - this simulates trying to shoot a gamebird (or squirrel, or whatever) in the head (or neck) to avoid wasting meat. Fill the recesses of egg cartons (preferably the plastic ones) with a plaster of paris mix, and insert a popsicle stick in each so it sets standing straight up. You then have a series of plaster knobs with a wooden neck, which are stuck into holes drilled into a wooden support (set horizontal to simulate a fence, or standing vertical to simulate a tree with the holes drilled at an angle.) Shooter must hit the 'head' or 'neck' without touching the support. Miss & Out elimination.
A bit of a variation on this is to set out raw eggs to shoot at. One dastardly version requires any shooter who fails to break his egg to eat it!
How about candle snuffing? String cutting?