One of my favourite subjects, partially inspired by my favourite video game (Chrono Trigger), is time travel. I love all forms of time travel and have made enough of a study of them that I jokingly call myself a Temporal Physicist at times. In doing this, I boiled time travel down to four major types, each with two sub-types.
Physical: You and/or objects travel to the future or past. Most commonly seen form of time travel. Messages from the future count for this type as long as it isn't a psychic message.
Mental: Only your mind travels in time either to your own body or another person's. Type of time travel seen in time loops.
Alternate Universe Split: This result creates a new universe where the changes happened, rather than changing the current universe.
Return to Home: After the time travel is complete, the traveller returns to his own universe, leaving the new one to develop on its own. Seen in Dragon Ball Z when Future Trunks returns to his own timeline after saving Goku and creating a new one.
Return to New: After the time travel is complete, the traveller visits the relative present day of the new universe; returning home requires the ability to move sideways in time. Taking The Slow Path counts for this version of AUS. Seen in Chrono Trigger whenever someone changes history (one such new universe seen in Chrono Cross).
Temporal Overwrite: This result changes the universe it happens in.
Memory Shift: The results of the time travel creates new memories in the traveller reflecting the changes s/he has made to the timeline. Seen in the movie Frequency whenever John changes his father's decisions in a way that impacts the timeline.
Time Orphan: When the traveller returns to the future he has no knowledge of the resulting changes of the timeline, which can include the traveller no longer existing. Seen in Magic: the Gathering when Sarkhan saves Ugin's life 1280 years in the past, then returns to a present where he was never born on Tarkir.
Immutable Fate: The time travel has no actual result.
Already Changed: The time traveller, whether or not s/he knows it, has caused the situation s/he went back in time to change or going back in time must be done because it was done; alternately known as the Stable Time Loop. Seen in Harry Potter and the Prisoner of Azkaban when Harry and Hermione save Buckbeak and Harry saves their past selves.
Unable to Change: No matter what the time traveller does, the timeline remains unchanged. This is either due to the traveller being unable to accomplish anything or because time manages to snap back to the original path on its own. Seen in the Sailor Moon/Ranma 1/2 fic Fist of the Moon.
Destruction Paradox: The time travel destroys things.
Destabilization: When the time travel changes something, its existence begins to unravel, getting rid of the object or person in question. Seen in Back to the Future, when Marty's family starts fading because of his interference.
Total: The time travel erases the universe immediately. Rarely used due to it making for a very short story.
Things get more complicated when these types are mixed, such as in Back to the Future, which has a little Temporal Overwrite (Time Orphan) mixed in, because any changes made in the past remain even if the time traveller is erased.