Bananas are great - easy to peel and eat. Berries, like someone else suggested. I love pears, plums, peaches.. not the easiest things to cut at your desk, but I just pick these up with a papertowel and eat them so my hands dont get all messy. yum!
I am guilty of buying the pre-cut melons but not just for the convenience. When they are pre-cut I can SEE them to see if they are ripe enough. No more wasted money on a not-really-ripe honeydew! If its too expensive to buy the ones in the deli, why not buy canned fruits like pineapple chunks (in their own juice, not in syrup). All you need is a can opener and a sink to drain it over.
You could also make a fruit salad on the weekend or whatever day you have time and then portion it out into smaller containers. If you dont have any - look in the plastic bags/wrap aisle for reusable containers or save cottage cheese, yogurt, margarine tubs. I'm sorta partial to the ziploc push n seal ones cause they really seem durable so far and really close well. I bought a set of 4 and havent needed to buy any more since.