"Fear Factor" was an American prime-time "reality" game show that ran between 2001 and 2006. The whole point of the show was to see how long someone could tolerate something frightening or gross. A children's party version needs to avoid anything dangerous but can elevate the "gross" factor that some children seem to enjoy.
Use black and yellow tape or streamers to rope off just enough space for each game. The black and yellow coincides with the theme colors of the game show.
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For a balancing act game -- fear of falling was a big deal on "Fear Factor" -- set up a 2-by-4 piece of wood on two cinder blocks. Each contestant must race back and forth across the wood. The wood is no higher than a foot off the ground, so even a bad spill should not be dangerous.
"Fear Factor" frequently had contestants eat something distasteful. Have the children compete to see who can hold a harmless hot or cold object in his mouth the longest, or bury something in a plate full of whipped cream and have the children retrieve it with their mouths. The object should be something "gross" but cute, like a gummy worm. You could have a contest with a certain amount of gummy worms in different plates. The kid who gets the most out of her plate at once wins the prize.
Create a bloody "Bob." Set up large buckets of water with red food coloring. Place some kind of food item inside and have children "bob" for a few seconds to pull it out.
Any kind of food challenge will do for a "Fear Factor" party, and kids can be repelled by things other than the insects the show's contestants had to swallow. Think about what the party guests prefer and what they might want to see their friends try to eat. Some general suggestions are some kind of baby food, something dyed in an unusual color, or even something healthy like liver.