One of the earlier titles by a developer that would eventually take the name Blizzard, The Lost Vikings starred a trio of, well, vikings. Flung through different time periods by a grossly incompetent intergalactic despot, the Norse trio raid and pillage their way to the exit of each era (thankfully history always has an escape door). While all three Vikings were playable, originally the player could only manipulate one at a time, meaning timing and action had to be just right in order to solve puzzle that required the characters work in tandem. Dying rewarded the player with a fiery Viking funeral, which was pretty damn metal for an SNES game. In fact, I wish more games would honor player deaths with flaming pyres on long ships. While the time traveling aspect of the game mostly served as a reason for different backgrounds and enemies, you did learn a few fun facts. For instance, did you know that Viking shields were strong enough to deflect laser fire? Whether that's because Vikings were ahead of their time in the shield department or the lasers of the future being disappointingly weak will doubtlessly be pondered further in the never-to-be-released-ever Lost Vikings 3.
The Blue Blur has blue blurred his way through several time-scapades over the years, because apparently just being really fast isn't interesting enough to keep the kids' attention. ITEM 1: Those sad few who spent most of their Summer job earnings on Sega CD system may recall SONIC CD, in which our hero is not only really fast but can also travel into the past and future. The impetus for this is a plot by Dr. Robotnik (or Eggman, whatever) to take control of a tiny time planet and use its time-warping properties to... warp time. One cool aspect of the time-travel mechanic other than slightly altering the levels was the ability to determine which future zone Sonic would visit depending on his actions in the past. The default outcome was a "bad future" in which Robotnik's inept rule created a bleak dystopia of industrial pollution that would depress the hell out of the Lorax - even the trees were artificial! However, by destroying the evil scientist's machines in the past you were rewarded by a happier future in which small animals frolic around the screen as nature intended.
Then there was Sonic the Hedgehog (2006). There was time travel in that.
Moving on, there was also Sonic Generations, in which Sega execs decided to make a game that appealed to our sense of nostalgia for the Sonic that was. The story imagined the chatty Sonic of today meeting up with his shorter, mute self of the Genesis years due to the machinations of a time monster Robotnik found in space. Also, you get to have a reunion with old, less-polygons Robotnik and old equally annoying Tails. Unfortunately, you can't alter the timeline to prevent the last decade of Sonic titles from being released, or keep your hero from learning language. However, if Sega's mission was to remind you how much fun the games used to be with a trip to the past then Mission Accomplished.
It could be argued that Tim, the hero of indie game Braid, is not really a time traveler. But it all depends on perspective. Sure, at first glance Tim is merely your average, well-dressed gentleman seeking to rescue his princess girlfriend from some terrible monster using an array of time reversal abilities - and jumping. But do Tim's abilities to alter the flow of immediate time make him a time traveler? Yes. And no. What if reversing time here is only an interactive metaphor for the need to revisit the past before accepting the present? Can a metaphor be time travel? And what if Tim himself is merely a symbol, a peek into our own psyche that seeks to elicit a bigger truth about the consequences of relationships - relationships to others, to games, to ourselves? Can a symbol use a metaphor to travel through time? I'll tell you the answer: you need to figure it out on your own. All answers are right and not right. Seek your own truths, man. Fight the power. Buy Braid.