A wide variety of vegetables and fruits grow well in a hydroponic setup. Salad greens, herbs, and strawberries are popular examples. Root vegetables need a specific type of setup to thrive. For example, a setup with plenty of support media that's deep enough to both support the plant structure and provide room to grow, combined with an ebb and flow system can support most root vegetables.
Even trees can be grown hydroponically. Many growers report better yield and better tasting fruit from hydroponics. Be sure to grow dwarf varieties in your hydroponics venture so they don't grow beyond your enclosure!