Never run away from the Time Police!
 

At the end of Star Trek: Voyager, the Captain Janeway of the future goes back in time to help the Captain Janeway of the past get her crew back sooner because 7 of 9 dies, and Tuvok goes crazy. Starfleet already frowns heavily on people disrupting the time stream, and Future Janeway's actions could have affected the timeline with potentially devastating consequences (bear in mind, the future turns out just fine with the exception of a few characters, they all got home).

So here's the question: Should people who receive aid from a future self, regardless of whether or not they accept it, be held responsible for the actions of their future self?

Well, that depends on which time travel rules we're following. If it's Star Trek time travel rules, then no, because by creating a new timeline you break the timeline you originally came from and send it in a different direction, and your past self from the new timeline doesn't necessarily need to fulfil a predestination paradox and come back and do shit—so there's no responsibility.

Terminator time travel rules, however, see things a little differently. There might be several versions of the same timeline, but in the end, whatever happens, the timeline corrects itself so certain events always wind up occurring. Judgment Day gets delayed, but still takes place, and John Connor sends back Kyle Reese and later a modified Terminator no matter what. This, however, raises the question of whether anyone following Terminator rules can be held accountable for any of their actions, as, seemingly, the timeline will correct itself to make the same rough series of events occur despite efforts to the contrary. It's a bit hard to decide on this one, as it deals with free will and destiny and the like.

Back To The Future rules work a little like Star Trek rules, with the exception that everything can be put back to normal if the world gets a little too muddled as a result of wacky time-traveling adventures. Given that restoring the timeline to its original state wouldn't be noticeable to anyone except the person/people who fixed it after screwing it up, nobody will know any different, and they certainly won't need to be reprimanded for their actions.

Lastly, I'll mention Primer's rules, which hold that causing the slightest discrepancy in the timeline will fuck things up hugely, and that sooner or later people will notice that bad things are happening. In those circumstances, as soon as anyone incurs a paradox of any kind, I reckon they, along with their duplicates, ought to be shot on sight, as by that point they could cause no end of mayhem simply by continuing to exist.

OTOH if you assume that they have no responsibility, then what deterrent is there to prevent people from going back in time and fucking with everything?

The most responsible thing to do as an observer in the present is to immediately kill the future self.

The question depends on what time travel conventions are observed:

The Marvel Comics general rule of time travel states that any meddling done by a time traveler splits the timeline off into a different direction. He will return to an unchanged future; his actions will just have repercussions on an alternate dimension. In this instance, you cannot hold his alternate self responsible for anything. Just the guy who mucked up the other dimension.

The Chrono Trigger rule of time travel, however, holds that the future is fluid, and time travelers are immune to any changes they make in the time line. (There's only one exception, Nadia's disappearance in 600 AD as a result of her own time traveling). In this case, you CAN hold Crono and company responsible for the thousands of people who existed in the ruined future, who are now shunted off to the Tesseract along with Lavos!

The convention observed in Prisoner of Azkaban is subtly different again. Here, there is just one timeline. Whatever happened, will happen. All time travelers will just end up making it happen. This creates a dandy time paradox of course, but in this case, you CAN hold the time traveler responsible for their mistakes.

But I haven't fully answered the question, did I?

In Janeway's case, she hasn't committed the crime yet. But she did knowingly change a timeline in which the Federation got hold of anti-Borg weapons. Because of future Janeway's selfish desire to save some of her crew, she sacrificed the acquisition of that knowledge. And may have doomed millions to assimilation. So, yes.

No, as disrupting the flow of time may not make that "future self".

Hitler as a baby paradox and all that.

Good, good. Now what if you accepted the help of a future self? Would you be an accessory to time crime?

Time crime is a funny rhyme...

And yes, you would be an accessory to time crime. Its no different than non time crime.