Looper this past weekend. While I found it to be a fun film with good dialog and an interesting premise, it ended up having many of the same problems as the majority of time-travel stories. There were inconsistencies and paradoxes, and plot holes, but the core issue is a very basic one: "Make it didn't happen" is a very unsatisfying story.
The basic plot of this kind of story is that a time traveler wants to go back into the past to change something that he didn't like. Right off the bat we have a paradox; if he succeeds then there's no reason for him to go back in time, and therefore he doesn't, and therefore he fails, and ... yuck.
Much worse though is when the protagonist of the story succeeds and therefore doesn't remember all of the horrible things he had to go through to succeed. This completely nullifies any character development in the story. Everything at the end is exactly as it was in the beginning. Really, this sort of story is no better than the ones that end with "... and it was all a dream."
If the past does get changed and yet, through some sort of literary hand-wave, characters remember the past that no longer happened, why don't others remember that same past? Is there a limit on the number of prevented pasts that can be remembered? How does this differ from being a stark raving lunatic?
Can a time travel story be written that doesn't lead to a paradox? Yes, though it takes some careful plotting.
The time traveler can be from the future, possibly with limited knowledge of the present, and be tasked with ensuring that history plays out like it was meant to (e.g. Terminator). He isn't trying to change anything and his actions in the story, no matter what, are already incorporated into the time line.
It also works if the time traveler is sent back into the past to retrieve objects or information rather than to change history (e.g. The Flight of the Horse by Larry Niven).
Alternately, having history "heal" is an interesting option. The time traveler can succeed in preventing a past event, but have something else happen that leads to the same eventual outcome (e.g. The Time Machine - 2002 version). In logical terms, this is the equivalent to having the time traveler's actions be already a part of history, but they're unaware of the exact role they played.
All of the above being said, I did enjoy Looper, though there are a lot of other time travel movies that had a much bigger impact on me.