I don't have a problem with puzzles; in fact, I rather like them because I like solving things. My problem is with a class of puzzles that I call "null-information" puzzles. These are puzzles that provide no clue what you have to do, what the solution may look like, nor do they provide any linkage or clue to any information that may be key to solving the puzzle. You are left to simply experiment randomly with no guidance until something just "clicks". The challenge of the puzzle is not in the difficulty of logically determining its solution but in the completely contrived obfuscation of facts necessary to solve the puzzle; you are left to randomly guess the mind of the developer. Such puzzles often require one to purchase a guide book or look up information on the web, something you should never have to do in a well-designed game. It's these kinds of puzzles that make me just pull out the axe and smash the door down(when I'm allowed to do so by the developer).
An example of what I'm talking about would be finding yourself trapped in a room with 3 switches on the wall with 3 different positions, up, down, and neutral/middle. It would seem obvious that the switches are the puzzle, and you have to find the configuration that opens the way out. You start pushing and pulling the switches with no clue which configuration opens the way out. Wrong configurations result in some horrible death, meaning you will be using the save feature a lot. With no clues to allow you do deduce the correct configuration, you get to spend your time trying all 27 possible configurations. Have fun! But, here's the horrible part of this puzzle. The switches on the wall have nothing to do with opening the way out; messing with the switches at all kills you. There's this weird, slightly discolored spot on the opposite wall, barely noticeable, that you are supposed to press to get out. If you had only spent time randomly clicking about instead of fussing with the switches, you would have lived and found the way out. *bleagh!*
That example sounds contrived, but it's precisely the kind of thing that developers put into some adventure games, and I've run across exactly this kind of puzzle at least once.
EDIT: Did my math wrong on the number of configurations. The number I originally had, 162, would be true if the order in which the switches were manipulated also mattered. If the order doesn't matter, then only 27 manipulations are unique. However, 27 manipulations still takes a bit, and you have to track which ones you have tried to avoid repeating. The end result, boring tedium, is still the same.