Rabbits actually don't need fruit. They like it, and it makes a good treat, but it's not good for them because of the calories, sugar, and water.
A real rabbit-appropriate healthy diet is a measured portion of commercial rabbit pellets and a generous supply of low-calorie hay, like Timothy or oat. I fed my meat rabbits plain pellets, with some feed supplements thrown in for the nursing females, but the males, who got no supplements, got a bit fat.
Their digestive system is built to take a monotonous, low-calorie, high-fiber diet, and they're really good at squeezing a lot of nutrition out of plain grass. Since it relies on a population of fermenting bacteria in their gut, sudden diet changes could upset their digestion. They might get gas, they might get diarrhea.
Not all household vegetables are safe for rabbits. Check this list over.
http://www.adoptarabbit.com/articles/tox…
Also, here's a list of rabbit-safe veggies and fruits.
http://www.adoptarabbit.com/articles/pac…
Not that you can't give your rabbit fruit, just don't make it a significant portion of his diet.