Where would we be without vacuum pumps?
The most obvious thing is that research into how pressure and fluids work would be severely retarded. Of course, this connects directly back to vacuum pumps, as such knowledge was used to make better and more efficient pumps. But that wasn't the only thing that could be applied to. Light was known to be a wave, but it could travel through a vacuum. How light could do that was eventually explained by the theory of relativity, which is used by GPS systems.
Vacuums are also used in light bulbs. If air were in the bulb, the filament could burn, which would rapidly extinguish the light. But more than that, vacuums are necessary for vacuum tubes (quite appropriately) which were vital in early computer systems, and vacuums are required to make parts of modern computers.
Understandably, things that will be exposed to vacuum (such as parts on the space shuttle) need to be tested to make sure they won't fail in those conditions. Also understandably, it's much cheaper to test those things on Earth. That means making a vacuum by means of a pump. Without the vacuum pump, no space program, as if the lack of computers wasn't a big enough hurdle.
Lasers work by exciting the electrons of a specific, very pure, gas (what gas is used depends on what frequency the laser needs to be). Vacuum pumps ensure normal air doesn't get in. Lasers have many uses, not least of all medicine, such as radiotherapy, which is used for treating cancer.
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