Strictly speaking, it's possible to grow fruit trees, corn, and watermelons in hydroponic setups, but sometimes they don't make a lot of sense, either economically, space-wise, or in some other sense. Corn is an excellent example - it's not a high-value crop and it takes up a lot of space for the relatively small amount it produces. Fruit trees can produce gorgeous, flawless fruits with excellent taste, but full grown trees can be difficult to manage, especially when their canopy spread is large. Dwarf varieties can be a good option, if your have the space.
Some particularly picky crops may not be worthwhile for hydroponic production. Radishes are a good example - they're inexpensive and available year-round at your local grocery, so it may make more sense to devote that space to an out of season crop or something you can preserve for later or even sell at a local market. Vining plants can also present unique challenges, since they can take up significant horizontal space unless they're trellised. But melons and squash all need additional support as they grow and mature. Vertical support systems for these plants can increase your available space, but they require extra expense and frequent monitoring to ensure the fruits aren't damaged and the support system can manage increasing load.
