A person who constantly feels obligated to follow a story you tell, with a worse one, making them sound like they've been through a much more terrible ordeal.
Susan: Today I slipped on the ice and cut my head open.
Tom: Yeah well, last night I slipped on the ice, broke two ribs, cracked my head open, AND my girlfriend broke up with me.
Susan: You're a story topper. It's lame.
A Story Topper is someone who tops every story with a even better version of one just told.
"Dude, i had to get this medicine for the little infection on right eyelid from my eyebrow piercing. It was crazy."
"Oh yea, last month when my friend got his eyebrow pierced it got really infected and you could see a bunch of dark green veins surrounding his eye."