Narbonic: the 'Dave Davenport is Unstuck in Time' arc codified the rules, and future story arcs used the same rules. Fiddling around puts you in an Alternate Timeline. To move through time requires all the eneregy of an entire universe, thus utterly destroying an alternate universe/timeline in the process. Since you are in an Alternate Timeline, you can indeed change the future or the past. Dave is able to stop smoking by never having started. He is also able to give his past self information that saves the lives of Helen and Artie, and avoids a Bad Future.
The Adventures of Dr. McNinja features time travel (as well as dimensional travel) in several arcs, including "Doc Gets Rad" (Big Bad Sparklelord gets defeated by being trapped in a Stable Time Loop), "Army of One" (In a flashback, a time-travelling Chuck Goodrich tries briefly to stop Doc from being cloned by Ben Franklin II), and "Space Savers" (Yet another Chuck Goodrich travels back in time [and into another universe] to stop a space dinosaur invasion). Since the comic works on Rule of Cool, the precise rules for how all this fits together are never clearly established.
Bob and George. Oh, lord, Bob and George. One of the recurring catchphrases shared by many characters is "I hate time travel". George even suffers a nervous breakdown when faced with having to use it.
The Dreamer features an odd case of time travel. Whenever the heroine falls asleep, she is transported to 18th century America in the middle of the American Revolution.
Dresden Codak has a major plot arch which revolves around time travelers from the future entering and later invading the present.
Earthsong features a particularly head-spinning variant that doesn't actually CHANGE TIME AT ALL.
Homestuck incorporates a lot of Time Travel in its plot points, especially with the Midnight Crew intermission, where every single member of The Felt had a special ability related to manipulating time or alternate timelines. Within the main story, Dave (as the Knight of Time) has the ability to accelerate or reverse time around him. Alternate Future Dave becomes a minor character, but he is doomed to die since he's not part of the alpha timeline.
A major source of humour in the comic comes from 'Trollian' a IM system of sorts used by the Troll aliens that can be used to talk to others, and yourself, from forwards and backwards in time. However the Trolls' grasp of time travel is tenuous at best, and it probably causes more confusion than clearing anything up. One particular troll spends literally hours arguing with his hated past/future self (there's one notable instance where he starts a time memo only to be interrupted by an argument with a future version of himself that goes on for so long he becomes that future version of himself and starts arguing with his (by then) past self).
After touching an artifact that once belonged to Lord English, John Egbert is able to teleport and time travel throughout the narrative though he can't control it yet. Unlike Dave and other Time players' form of time travel, he can actually change the past instead of simply spawning a doomed timeline or fulfilling a Stable Time Loop.
The current mega-arc of Irregular Webcomic! has massive time travellings done by many many characters in many many themes. This might be a Gambit Roulette on the part of the author to resurrect himself and Screw Destiny after he got killed by himself in the future and becomes Death of Going Back in Time And Killing Yourself and is suppose to go back and kill himself to continue the Stable Time Loop. Also, Leonardo da Vinci is a time traveller, is British, and made deals with Deaths. Did I mention that TARDIS also exist, and being used by the pirates and British navy crews (the latter owns it (?)), with the theme sets in 18th century? Yeah, it's that weird.
In Genius: The Transgression, time travel is possible, but it's almost never a good idea. There's an entire section devoted to time travel and results thereof.
In Girls in Space, whenever the girls find the Earth, it is a different time period. They have no control over which time period has appeared.