As a player who is taking up the King's Indian Defence vs 1. d4, I was surprised to learn from chess forums that some 1. d4 White players really dislike the typical KID player.
After some digging, I found that it is because a typical KID player is one who plays not for the material of the pieces but plays for the initiative, which usually results in unclear, dynamic play and sometimes absolute chaos can result on the board if White chooses to take on Black tic for tac.
What of Kramnik's infamous Bayonet Attack? Sadly, that line has gone out of fashion as Black players started to devise counter-plans to achieve equality (partly in due to the modern 7.... Na6 variation), taking the whole sting out of a queenside attack.
I know at my club, some 1. d4 players absolutely dread the Nimzo-Indian Defence because the darn thing is so hard to crack and right from the 3rd move, Black is threatening to unbalance the game with 4... Bxc3. If you throw in the Rubinstein, the Saemisch, the Leningrad, Romanishin then suddenly the Nimzo-Indian starts to look really really daunting.
As for 1. e4 players, some players dread the French Defence, it's rock solid and allows Black a transition to the middlegame. White sometimes play the f4 variation to stifle Black and attempt to put Black out of his misery but there's still plenty of play on both sides. The Winawer and the MacCutcheon variations offer Black plenty of counter play as well.
How about the Najdorf Sicilian? Bucket loads of theory and play is governed by move memorisation that it's downright scary.
Using computers for openings is next to impossible. A dated study done by Chessbase shows that computers are strange beasts when it comes to openings (hence the need for opening books) - see inset.
What openings do I dread? Well.... none at the moment. I play all kinds of openings so I'm not that disturbed by the different types of opening play.
Do you have an opening that you absolutely hate facing?