Actually, time slows down with any acceleration. Atomic clocks aboard planes have different readings when compared to those on the ground. The difference is very small, so we don't notice in everyday life.
Gravity warps space-time. Satellites orbiting the earth are actually accelerating towards the earth. So time slows with Gravity also.
Relativity says we can never exceed the speed of light, time slows so much that it becomes impossible. At the speed of light, you would be instantly transported to your destination, because time would not exist for you. How can you exceed an instant?