Most problems with reptiles happen due to poor care, so if you do everything right you won't need a vet. Although it is suggested to bring a fresh fecal sample to the vet(can be anywhere from 15-30 dollars) every year to check for parasites, and you can give the animal the medicine yourself if they do have parasites. Though parasites are excreted through the feces--so often times if you keep the cage spotless and don't let the gecko walk through his own filth he can often flush out the parasites himself! :) But if it gets too bad of course, don't hesitate to take them to the vet!
If it's something you would go to the hospital for(broken bones, large gashes in skin, infections, etc) then take it to the vet. You can often post on a reptile forum (or PM me) and let me know the care of the animal and see if it's something they can get over at home. For instance--small injuries can be healed with warmth, clean cage, and neosporin without painkiller! :D