For Monopoly, mathematicians have worked out winning strategies. I think it has to do with a high chance of people landing in jail and the odds of landing on fields when starting from jail.
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).
That's testable. Simulate a few tens of thousands of games based on some criteria (players always buy properties they land on if they can afford them, players will mortgage their portfolio to buy properties if it blocks another player, etc) and see if the person winning on round n where n is an early round is the same as the person who's winning at the end of the game. It certainly sounds like it's true. It'd be interesting to see how early you can abandon a game and still know who'd have won.
Monopoly's lack of fun comes from the player elimination, which is a crucial part of the game. People dislike player elimination (because it feels mean), and include stuff to avoid it, (fines go in the middle and are collected if you land on free parking, for example). These house rules turn a 1 hour game into an interminable 5 hour slog.
If you have a group of people who are happy with the concept of player elimination, and who play to win, and you avoid the house rules, Monopoly becomes somewhat fun. But there are very many much better games.
No. The game is, just kill me and win. Stop trying to prolong it.
What makes a game interesting to most people is how much randomness there is.
Human brains are built to dole out reward hormones when they make predictions and, followed by a period of uncertainty/expectation, their predictions come true; OR fail in such a way that they gain enough information to improve future predictions.
Having too little randomness can (if there is little complexity) mean that predictions always come trivially true, which does not trigger the reward mechanism.
Having too much randomness disables the triggering by way of a "teaching failure". (Though it still leaves the way open for the success trigger, thus addictions to gambling.)
So in order for a game to be good, it needs to strike a certain balance between simplicity/complexity and determinism/randomness.
I've played a few games where someone managed to win after only a couple of turns, or I just roll busts over and over, but there are still plenty of opportunities for strategy in between those wild swings of good and bad luck.
Because it often makes it unfun. Not always, of course, many of the highest rated games on the Geek also have random elements. But in the case of, say, Chutes and Ladders, the entire outcome is random. Might as well flip a coin and call it. Why spend the time going up and down the board?
For monopoly, a big crime is that it takes a long time to lose. You can spend an hour with no chance of winning, kept alive only by random chance.
These are not 'unworthy', they are just boring in comparison to many other games. I think people avoid the 'other' games not because they have some deep subtle appreciation for the merits of the 'bad' games, but because they haven't come across better options. It is rare to find someone who likes Monopoly who can describe another game with the same theme (not counting Star Wars Monopoly!).
...and when the first player loses, they have to sit by and idly watch while one player gains a larger and larger advantage, only waiting for the rest to lose.
I think the boardgame geek top list is a bit biased, because it was made by gaming geeks who might tend to prefer complicated game mechanics.
Okay, you have to be into heavier games to be into Brass, but heavy Euros are hardly the be-all of board gaming.
[edit: Yeah, I take back the 'I don't think so' - on reflection - there is a bias towards heavy games at the top, but I don't think that's why Monopoly, Parcheesi et al are low]