And finally (for now), opposed rolls: The player and the GM both roll. Your roll becomes the target number for the other side. This is a broad enough category it's really a separate post.
Victor, a Rascal certified game designer
Roll vs GM resource: The GM has a variable pool of points they can spend on the target number. The GM decides how important each roll is to them and spends some of their resource on the target number. Players can manipulate the pool as well, for ex reducing it before an important roll.
Roll vs fixed target number: The game designer does the work for you. They've figured out the best target number (or numberS, like in Apoc World) for the experience they're designing for. Simple and clean I like it.
Roll vs player resource: Your target number is how much food you have left, how much money you have or how good your reputation is. It's a known number that can be manipulated before the roll. Want to succeed? Better go improve your reputation!
Least favorite first: GM picks the target number from a list of examples. Games with detailed skill lists tend to do this. I still think it's boring, but it's less arbitrary.
I think it's bad form to discuss problems without also discussion solutions.
A thread of alternatives to "GM picks the target number."