For me, I usually eat a ton of things and don't have a problem trying new things but:
Bananas - something about the texture and taste of a ripe banana makes me gag.
Papaya - apparently, I used to love this stuff as a wee child. (Baby food?) Now it just makes me gag - I think it's the texture combined with it's instant laxative effect for me. (I will eat the dried cubes in trail mix.)
Cranberry cocktail - I instantly know why I hate this so much now. I used to get urinary tract infections from HELL, and I constantly had to pound this stuff to get my system back to normal. Now, I can't even drink this without gagging. (It's always so tart and astringent.)
Wonton soup - Chinatown uses a chemical to season the soup OR meat mixture, but if the chef goes heavy handed, it tastes like chemical warfare in a bowl. I had the misfortune of getting some in a restaurant about 15 years ago, and I haven't ordered it since.
Cilantro - I'm one of those people who taste it as soap. However, if it's buried in other stronger flavours, I'm fine with it - I can eat cilantro in a soup OR as a seasoning, just don't let me taste it first...
Melons - every melon makes me gag. You know those summer fruit salads? Yeah, mostly ick...