Strength Competitions
-------------------------------
Hanging from the broken Bridge of Khazad-Dum (longest time wins)
Hanging in the heart of Mount Doom (longest time gets most points [wins])). One-handed hanging doubles your points!
Other
-------------------------------
The Peg-Pounding Event (How quickly can you bang all the pegs in the Party Field into the ground?)
The Beacon of Gondor Climb (How quickly can you climb to the top, light the beacon, & make it back down?)
Marksmanship
-------------------------------
Rocks- Hit the stuffed Gollum in the head & win!
Rocks- How many Uruk-Hai can you hit in 1 minute?
Apples- Hit the stuffed Pippin in the head & win!
Rings- Throw the Ring in the tiny Lava Lake & win!
Kicking- Take turns kicking Gamling's beer over-whoever gets him the wettest wins!
I could think of a few marksmanship competitions involing Gimli & a few Uruk-Hai, but I don't think I'll include those
...