Gravitational waves travel at the same speed as the speed of light in a vacuum, in general relativity. In special relativity, this is the maximum speed for any interaction in nature.
If gravity was faster than the speed of light, then predictions we make according to the bending of light would be incorrect.
If gravity was faster than the speed of light, then the orbits and positions of the planets would be completely different.
Those are my two main points, to help me prove to you that gravity travels at the speed of light.
Also, light is not the only thing in the universe which travels at the speed of light. It is about all massless particles! Photons and gluons are two good examples I can think of of massless particles, I'm not sure about gravitons though - but I'll still include them.
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