I listened to a Drew Carey interview once.. the man is passionate about Monopoly. I don’t think there’s too much strategy there besides “don’t let property go unsold” and “hoard houses” but he disagrees.
The in the box rules state that every property must go to auction on first landing if the player refuses their option to buy it at face value. There's a lot of strategy possible in auctions, but a lot of house rules don't like the auctions and either avoid them entirely or make them much rarer than the in-box rules state they should be. (In part because early and often auctions increase the cutthroat feeling earlier in the game, whereas a lot of house rules are about pushing the cutthroat stuff off later into end game.)
As long as you're using the correct rules and everyone is playing the game fast, they know what they're doing, and they're competitive, the game can be quite fun. It's also a lot less time intensive than many other board games where lots of people are negotiating.
If you play Monopoly and you don't trade, you haven't really played. And I don't mean all of the wacky trades that some families do (although I'm not against that), I mean trading money and property with other players. The two keys are:
1. In all games (not just Monopoly), people who cooperate win. If you make a mutually beneficial trade with another player, even if that player gets the better end of the trade, all other players lose ground. If you cooperate with another player by trading whenever there's any reasonable opportunity, the game is between you and that player; no other players will have any chance of winning. If you trade with everyone, and they don't trade between each other, you will inevitably win. Cooperation is making 1 + 1 = 3. No matter how that remainder is split, the more you get in on that split, the more ground you're gaining. Jump in front of every trade offer and offer a better one.
Almost every player that I've talked to who doesn't understand how Monopoly is a good game (and I've had a lot of Monopoly discussions) is completely incapable of understanding how a trade that gives somebody else a Monopoly can result in you winning the game. They look at you like you're stupid when you say you do it all the time. We live in a sick, atomized and alienated society. Getting the property that completes somebody else's Monopoly means you have a good basis for friendship.
2. You may do a lot of little trades during a game, but inevitably you are building up to the big trade which is your big gamble. You've calculated all of the probabilities, you've judged your competitors positions, and you're going to offer another player (or maybe a couple of other players over two succeeding trades) a huge trade which will set the conditions for how the random endgame will play out. You've made it look like you're giving the other end of the trades a chance, but you've calculated ahead of time that you've maximized your own chances. If you're playing against naive players, you'll always win if you do this first and you know what you're doing. If you're playing against someone skilled, it's a question of who calculated the odds better and whether the dice hate you.
edit: Another game with a similar feel and a similar benefit to cooperation is Container. A good game to soften up people who don't know how to trade is Bohnanza. A game designed to show aggressive cooperation is So Long, Sucker, which requires you to cooperate to be in contention, and requires you (mathematically) to betray someone's trust to win.