Mechanic with a rap sheet
I think that the game mechanic that has the worst reputation is roll and move. I didn’t dig into it too deep, but it's probably because there are a few very popular games out there that bad enough to leave a bad taste in your mouth.
What
Roll and Move, or Roll/Spin and Move, means that you roll dice or spin a wheel and use the result to move one or more of your characters. In most cases, dice will be used, but there are pretty interesting inventions in recent time.
Why
Why indeed? Well, it's just plain and simple mechanic. Remember Snakes & Ladders? While you might remember it as a game, it's more of an activity, since you don’t have any control of what's goes on in the game. The players are just spectators and if the game could roll the dice by itself, the players could just come back in 10 minutes to see who won. But this is also the mechanic strength, you can teach a 3-year-old to play games like that. They will lose interest when they grow up a little, but still it’s a good enough reason.
For Example
The worst culprit is probably Monopoly. This 1935 game, that was originally published in 1903 to show the public why monopolies are a bad thing, came to fame when parker brothers bought the rights for it. The game features an auctioning mechanic that is often overlooked, and so player just roll a die and move to a location where they can buy it or pay to the owner for passing there. The game offers very limited choices that when coupled with problems like runaway leader, and player elimination, the game “charm” wears off pretty quickly.
This does not mean that roll and move are simply bad, it just means that you need to tread carefully when you incorporate it into a game.
Jamaica is another simple racing game, where player are pirates racing around the island of Jamaica. In its turn, a player holds 3 action cards with 2 actions on each. Actions are move forward, move backwards, gain food, gain gunpowder and gain gold. The player then rolls 2 dice and need to deice to which action card to assign them, and in which order. Then all other players can select their own action card, but must adhere to the dice order.
While roll and move, definitely used here, the player has a lot of control over what die to assign to which action. Cases of bad luck can happen, and the game is absolutely luck based. But the main thing is that you have enough decisions to make you feel you are in control.
Camel Up is another racing game, but instead of actually racing, we place bets on camels in a camel race. The game has an interesting mechanic where camels, who arrive to a space where another camel is already on, climb the other camel. When the bottom camel moves, it will also carry all the camels on top of it.
In this game, each camel will move according to a roll of its corresponding colored die. Players will bet which one will win, lose and be ahead in each leg of the race.
This is again a roll and move, but since all players are effected from a camel move, you don’t feel that the “bad luck” you experienced is yours. It's actually you just made a bad bet. This separation of your action (betting) from the luck (moving a camel) is what makes the game feel fun.
It's still very much luck based, but in the spirit of betting, it's just fun.
Lastly, let's take a look at the game Survive: Escape from Atlantis!. In this game, all players control a group of meeples that begin on the island of Atlantis, located in the middle of the board. As the island breaks apart, they will have to direct their meepls to shore by making them row boats or swim to safety. The waters around the island a littered with monsters and the chances of everyone surviving are slim. Each turn, a player will roll dice that will determine his action. It could let him move a ship, but it could also allow him to move a monster. You might advance one of the boats you control, move a monster away or attack another player and eliminate the competition.
As expected, this game is also luck based. But here you always have something to do with the roll. You might prefer getting one action over the other, but the dice result will always benefit you. Sometimes more and sometimes less, but the fact that it's always positive takes away the bad luck feeling away.
So is roll and move that bad. Actually, no. When it's not the main mechanic in a game, it can be funny and light. When it is, it should probably affect all players and not just one so no one will feel unlucky.
If need be, keep the game light and short, so players can enjoy even on a bad luck streak.