For starters, the largest piece of evidence in our solar system: The Sun. All light is a form of electromagnetic wave (radio waves, microwaves, and x-rays are a few of the others) and if electromagnetic waves did not travel in a vacuum, no light from the sun would ever reach us here on earth.
Knowing That Interplanetary Space Consists Of A Vacuum, What Is Your Evidence That Electromagnetic Waves Can Travel In A Vacuum?
The sun reaching the earth is not evidence of a space vacuum. Based on that reasoning, there would be a convergence of radiation from all the stars encircling the earth, producing heat death. That is not what we observe. The level of radiation reaching the earth is attenuated. Otherwise the earth would be like Mercury. Really hot!