I love time-travel as a plot element. It's pretty confusing and creates all kinds of complex questions about its logic, but it also frequently sets up stories that appeal to me. Characters get to meet historical people, or past/future versions of their friends or enemies, or maybe they see dystopian alternate timelines. Since these kinds of scenarios intrigue me, I tend to forgive all the messy issues around time-travel.
Any kinds of time-travel rules are fine enough for me; stable timeloops, people vanishing because of a temporal paradox, or whatever. Although I do feel like DBZ's method of time-travel creating alternate universes seems like the most coherent and logical option I've encountered (I haven't seen Super though, so if it addressed time-travel rules, I don't know anything about it).
I have a guilty pleasure for Peggy Sue/time-travel fix-it stories in particular. It's common in fanfiction; a character ends up sent back in the past for whatever reason, and since he's armed with future knowledge, he tries to use it to his advantage. He carefully maneuvers through the events attempting to prevent various upcoming deaths or disasters, and he tries to defeat the villain faster than in the original timeline. Often the time-traveler's actions may force other characters to respond in new ways, which can create unforeseen scenarios that derail the plans.