It depends. Many diet plans recommend no more than two servings of fruit per day since, as you pointed out, fruit is full of sugar. Other plans allow unlimited fruit and veggies between meals. Personally I think a minimum of two servings of fruit per day is good. But that's more from a health view than a weight loss view since fruit is a great source of vitamins and soluble fibre. And the sugars in fruit are a great energy boost. Fruit can be a real pick-me-up as a three o'clock snack, something you won't get with carrots.
When it comes to weight loss, it depends on if you're following a rigid program or not. If you are, then see how fruit can be incorporated within it. For instance as far as I know all fruit is forbidden in the first two weeks of the South Beach Diet. If you are counting calories, however, you can factor in as much fruit as you like provided you a) don't go over your calorie allowance, and b) you still eat other foods to give you all the other nutrients you need. If you're just combining healthy eating with exercise without a rigid program then you can just see how you go. Eat as much fruit as you feel like then see what the scales/measuring tape/fat calipers have to say. If you gain weight doing it then cut down, if it helps you lose weigh then keep going.
One thing I do recommend is to rinse your mouth with water or chew sugar-free gum after eating acidic fruits as the acids damage tooth enamel. However, don't brush your teeth immediately after eating acidic fruit or drinking an acidic fruit juice, soft drink or smoothie. The acids soften the enamel which is further damaged by brushing. Wait half an hour for saliva to neutralise the acids before brushing.