Chronology , a side scrolling puzzle platformer where you go between time periods to move about. A bridge may be broken or not yet built for example, so why not go to the time period when it's in operation?
Sonic CD. Sonic The Hedgehog side scroller where each stage has a Past, Present, and Future version with numerous changes. If you destroy the machinery in the past, the present and future will be altered.
The obvious
Braid , a puzzle game where you change the speed of time or rewind it to solve puzzles or get through some basic platforming sections.
Prince of Persia Sands Of Time ,
Warrior Within Two Thrones, and
Forgotten Sands. Rewind time to help you get through sections, or simply just not fail falling down into a pit.
Project Temporality , a one person co-op I like to call this type of game. Where you and past versions of yourself can accomplish goals as those temporal clones carry out the actions you performed and still alter the game world just as you once did.
Other time based puzzles exist such as slowing things down or events changing based on where you view them in the world.
Thinking With Time Machine , a Portal 2 Mod whereyou can create a temporal clone of yourself to carry out actions you just did. Another one person co-op.
Achron , a RTS with time travel story and manipulation for resources and troop control.
TimeShift and
Singularity , two FPS with slowing things down or speeding them up or freezing people in time. The later has two time periods which made it interesting enough story wise.
Zeit² , warning it has the Tages DRM, but gameplay wise a shoot-em-up where you can combine shots with your past self is a whole lot of fun. Tages is still terrible though, get it on Xbox 360 instead.
The Misadventures of P.B. Winterbottom , another temporal clone game as a side scrolling puzzle platformer. Constantly keep creating clones to help you get ever farther in the stages.
