It pretty much depends on how much time do you want to spend and how big your group is. Those are some of my ideas:
Creeper Soccer: Build two simple structures (boxes will do) Make sure you use obsidian floor (unless you wish gaps) and highly blast-resisting materials for the structures. Just like soccer, arrange the players in two teams, one goalkeeper each. Then drop a single creeper on the middle of the field. Armed with bare hands (or a simple stick), players havr to lure the creeper into the enemy goal, and make it detonate there. If it detonates somewhere else, spawn another creeper. If a player dies, it has to wait (let's say 30 seconds) to join the match again. You can change the rules as you wish as it is a very simple game.
Mushroom Hunt: it's mushroom season and everyone goes into the forest to gather some! Pick a forest area (quite big) and enclosure it with fences. Then, place some mushrooms into the forest, just like easter eggs. Also make sure there is a door to leave the enclosured area. Every player has got a chest outside the area. Basically, the player with most mushrooms wins.
But beware! To make it a thrilling game, there is a troll loose in the forests! The troll is equipped with a decent sword (stone for longer pursuits, iron for shorter). You can also give him vines to clim up trees. If the troll kills a player, that player is out. The troll can keep the mushrooms the player was carrying and save them in his chest hidden in a log. After a set amount of time (5-10 minutes will do), the player with most mushrooms wins. Of course players can't steal from the chests (not even the troll one) and the troll can't normally gather mushrooms.
-Human Hunt: Everyone goes into a big, enclosured forest (just like in mushroom hunt) and have to survive the hunter, a player equipped with stone sword, bow and arrows. The last one standing wins.
-Salmon Race: You just need a waterfall and two boats to play this. There are two game modes: Being the last salmon staying in the top of the waterfall (going outside the water flow counts as a defeat) or being the first one to climb the waterfall. Matches will either be really short or really long, depending on the waterfall, luck and skill