Grapes, apples (apples are my 'go-to' fruit), and bananas travel well and can be eaten without mess (the messiest part is what to do with the banana peel).
Though they are calorie-dense, dried fruits can be useful in a pinch. You can also let them soak in some water so they rehydrate some, so you won't eat as many as if they were completely dried.
Many other fruits---pears, peaches, nectarines--are a bit juicy to be eaten without mess, but you could plan for that and take some napkins and wipes. Of the three, pears probably don't travel as well and get bruised more easily.
You could also blend up some fruits with some kind of milk and make smoothies, packing them in a leak-proof container with some freezer packs in a portable cooler.
Juices are an alternative, but not the best (they are not whole foods, are calorie dense, and are usually heated, destroying enzymes). Make sure you get unsweetened juices if you go this route, and avoid 'juice drinks,' which have other ingredients (often HFCS) in besides juice.