You actually just cited my two examples of rampant dice roll luck.
Monopoly is easily my least favorite board game, utilizing luck in both linear movement (which stands for a lot in respect to property purchasing and paying) and the cards, which are collected at random. It's a game with the semblance of strategy and purposeful movement, but luck plays so big of a roll that there's never enough decision making to be interactive.
Mario Party, as fun as it is, is a game I've played dozens of times with dozens of friends, but despite my massive coin grabbing (due to expertise in gaming) and decent strategy, have never won. The luck element is so skewed that no amount of skill or practice will give anyone the high ground.
That makes it a good family game, one that can allow young people in to feel faux accomplishment, but it is truly poor game design. Complex elements of gaming can be demonstrated without relying too heavily on luck.
Want to play a real game that requires strategy but still has a heavy luck element? Play Carcassonne with me. The game is easy to grab, easy to learn, has few move requirements, but still has enough of a luck element that after a certain point of playing, everyone gets to even ground based on their skill. It's tough to explain, but it's perfectly balanced in that regard.
At least with random card choosing, cards are usually stored and played when advantageous. Cards can also have multiple purpose and effects. Dice have numbers, and those number are usually for a singular application.
Another game I hate: Risk. Little strategy, lots of luck. I'm not asking that every game be an abstract strategy game (Chess, Checkers, Go, Tic-Tac-To, Five Stones, Rock-Paper-Scissors, etc.), but for goodness sake, a game without a prominent mentally-driven maneuver is a slot machine.