1.  Chaotic Stupid (Neutral) as an excuse to do evil/ridiculous/insane bull$**t.  I have seen this many times and I am sick of it. 
2.  Lawful Stupid Paladin.  Thankfully, this has become much less of a problem in 5E. 
3.  Slutty Drow Priestess/Assassin. 
4.  All dwarves are ugly, the women especially.
5.  The "lone wolf" who demands hours of solo time and won't cooperate with the party.
6.  I'm too sexy for my shirt / Too sexy for my shirt / So sexy it hurts
7. The useless, lame-o character who contributes nothing and stands idly by while everyone else is desperately trying to survive in combat.  You find yourself praying a higher power will smite this player from the game because they are more useless than tits on a boar.  This one is not really a trope, just a personal pet peeve.