One of the amazing things about hydroponics is that it is so open ended. You can grow almost anything, it's just a matter of getting it fine tuned a little and often that's not even much of a problem.
I've personally grown tomatoes, cucumbers, peppers, lettuce (several varieties), beans, herbs, strawberries, corn, egg plant, and squash. Some plants don't like to be grown with others because of different nutrient concentration preferences. For example lettuce runs at a lot lower nutrient concentration than tomatoes. But as long as you check it out you can generally grow it. I remember being astounded that you can even grow roots crops and I actually grew a rather stubby carrot one time and people grow potatoes.
If there is a way to grow it in dirt, there is likely a way to grow it hydroponically. That is simply great fun!