There are many things I dislike about Monopoly but the randomness isn't one of them. A good deal of games I love have a big chunk of luck/randomness and I'm fine with it.

The things I dislike about Monopoly:

* Not too much strategy involved. The player who wins is usually the one who buys a lot of lands early.

* It's long. Even the shortest games last over 90 minutes. However the winner is decided much earlier in the game. There's very little you can do to prevent an early leader from taking the game, and you have to sit there watching them bully you slowly for several hours.

* The theme sucks. "Buy land, make more money". I don't find that particularly fun.

* The good elements of monopoly are often found in other games that don't share the same bad elements (I'm thinking of Settlers, but there are others too).