After seeing Rian Johnson's Looper with some of my favorite movie loving people conversation expectedly spiraled into whether or not the movie handles its time travel consistently. In ways Looper is like Back to the Future, choosing to use time travel to tell a compelling story, but not a story explicitly about time travel. BttF was completely unconcerned with establishing rules, and the few it does establish, well Doc just figures "What the hell?" and they get broken anyway. Obviously BttF plays a lot looser than Looper, but I think it has a similar view. That's unfortunate, since Looper not only wants to take itself much more seriously than BttF but because the movie also focuses on the philosophical elements that pop up in more serious time travel scifi stories: can you change fate? Indeed, it's a problem fictional characters have been dealing with since Oedipus and beyond, though obviously replace time travel with prophecy for the ancients.
Two movies have been released in the last few years that actively talk about that issue as strongly as Wells in The Time Machine, and in the wake of them something about Looper's execution feels lacking. Shane Carruth's 2004 mind trip Primer and Nacho Vigalando's 2007 Spanish-language mystery Timecrimes take very different approaches to their time travel, but both follow their own rules perfectly.
They are movies that are about time travel just as much as they are about their plots. They also answer that eternal question completely differently.
In Timecrimes, Vigalondo fully commits to the idea of predestination. In that regard there is only one timeline in the movie, and it works so well because we follow the main character, Hector, as he bounces around that timeline, slowly realizing that his attempts to fight fate are exactly what's causing all his troubles anyway. Everything that has happened must happen (and already has, in case you're wondering about a certain callback in the third act, yes the hand is there in the earlier scene). Of course, if you don't buy into the predestination and single timeline theory, you'll have problems accepting the movie, which is why quite a few people favor Primer (though claiming Timecrimes is a rip-off is pretty silly, they are trying different things and both achieve their goals). I don't, so I'll point out that Timecrimes is available to stream on Netflix and has a better rating on Rotten Tomatoes.
Primer takes a different route. You can change the past in Primer, though you probably shouldn't. Primer is also notable for it's answer to the grandfather paradox being "yeah, whatevs" and ends with two time travelers living in a timeline where they never built a time machine and one of them promising to actively stop the versions of them that live in that timeline from doing so. Of course, it also comes to similar conclusions on causality and predestination. It's a much more confusing ride than Timecrimes, and not just because there's at least nine different timelines. (I should point out that I think Carruth is a better director than Vigalondo, but I favor Timecrimes for bieng more straightforward, they are both excellent movies.)
In the Doctor Who episode The Angels Take Manhattan that aired just last week the Doctor says that once he knows something is going to happen then it has to happen. Timecrimes agrees. Later a character proves the Doctor wrong. Primer agrees here. That character's actions then cause a universe changing paradox that the universe heals with desired results. That last bit is what Old Joe in Looper is counting on.
It's worth noting that the physical mechanics of time travel in Primer and Timecrimes also function the same: a stationary machine that sends whatever is inside back in time, but only as far as the temporal point where the machine was first turned on where the thing inside comes out (Primer, to either its credit or detriment, at least tries to offer a scientific reason for this). Looper's machine(s) send whatever is inside back exactly 30 years (to before time travel was invented) and to a predetermined position outside of the machine (which does not exist at the other end). So it's a bit more like Terminator -- a franchise that doesn't take it's time travel seriously at all -- except here inorganic matter is sent back as well because the Loopers need to get paid and the audience doesn't need to see naked old Bruce Willis.
So where does that leave Looper? I'm not sure, and neither is Rian Johnson. Predestination and causality are handled unevenly throughout. Body parts and people can be grandfathered out of existance, but the very act of Old Joe escaping his execution should stop him from going back in time at all. The movie sidesteps this concern with talk of fuzzy memories and cloudiness -- a timeline in flux. Like a photograph in which people are slowly fading out piece by piece, it's a distraction to try to stop the audience from asking questions.
And that's fine.
Looper is a great movie, even if it doesn't make sense. It could have, if they tried a bit harder (Primer's Carruth worked on time travel special effects in Looper, but not on mechanics, which would have made a very different movie). So watch it, and you might get tied up in conversations about time travel, but just think to yourself "it's just a movie, I should really just relax" and move on. Or better yet, remember Tom Wilson, who played Biff in Back to the Future and his song: "It's a movie! Stop asking me the question."
But if you want movies that actually make sense with their time travel, just watch Primer or Timecrimes.