"Imagine you could travel through time. You would never be poor again. You could meet anyone you want. See anything you want. Do something illegal with no consequences. Own a dinosaur. Kill Stalin (Hitler is too mainstream). Meet Stalin, kill him with a dinosaur, do something illegal to the dinosaur, then steal all his money"
I've played a few games, or homebrews ruleset of games that try and deal with time travel. Usually it ends up a pretty awful mess, with confusing rules, or the time travel happens infrequently as part of the plot. One game I have played where this isn't the case is Retrocausality.
Retrocausality, by Paul Ettin, winner of the Origins award in 2317*, has the mechanics to play out that classic scene from Bill and Ted where they need a key, so they go get the key later, after they break out. Skills are separated into two separate groups, one dealing with stuff non-time travelers can do (hacking, gymnastics, and animal training) and time skills for doing wierd trippy time travel things. Retrocausality is a diceless games, so instead of dice for rolling, you pull from a deck of cards. Normal skills are resolved in a somewhat traditional manner, adding your rank to the number of the card pulled, with face cards having various special meanings, and comparing it to a difficulty number. Time skills work in a more macro way. Time skills are put into four broad categories, which is further broken down into four types, each corresponding with a suite of the cards. Getting a key to get yourself out of a jail cell by placing it there after you break out probably falls under History:Club, which is borrowing objects throughout time. If you pull a red card, its a failure, a spade, a partial success, and a club means you are completely in the clear. Individual characters have ways of getting additional draws and other ways to increase their success, but that's the basic mechanic.
The pdf is layed out very well, with great explanations and colorful retro-science illustrations.
Its a really fun game. The time I played, we went forward in time, just in time to cause enough events to change to witness our future selves murder. We of course, didn't enjoy that, and went on a whirlwind adventure to save ourselves. Let's say the paradoxes didn't end there.
To be clear, this is very much a storygame. Those of you looking for a tactical simulation will be very much disappointed. This is also a game you have to be "on" for. It doesn't work if you just put in a twelve hour shift and just want to roll some dice (or pull some cards).
In addition to the core book, Paul Ettin has put out a first adventure for you potential time travelers. Both the rules and the adventure are available on DriveThroughRpg.