Multiple reasons:
1) Less bending over, which is good when you have a bad back (you still need to bend over, just don't have to get down on ground level).
2) Keeps wild rabbits OUT. I still have coons that steal tomatoes but we have a ton of rabbits that would decimate everything if it was on ground level, since I never fenced the area in.
3) Helps me control the soil, everything from improving drainage (the area my veggies are in is boggy, so this is necessary to allow for drainage) and for controlling the soil quality. I learned my lesson - soil matters! - and bought a bulk shipment of an expensive, locally made organic soil mix. I also have compost bins on the side (yay chicken poop) so I can naturally augment the soil over time without fertilizers. Guess it works because my mother-in-law, an avid gardener, kept commenting that my plants matured faster than hers and were 2-3x bigger than her plants of the exact same type and age.
4) I like the look of raised beds. Even though my set up is a little homemade (me and a hoe got it done) it still looks tidier to me than if it was all ground level.