That depends on which hydroponic method you are planning to do. Many terrestrial plants do not do well with their root and/or crown submerged in water. Most would require a part of their root exposed to air (some portion of the lower roots can be submerged, but not all). However, if you could setup a rack system whereby you put plants in water absorbing medium, which soaks up water from the fluid pipes, most plants can be supported with that system. There are also other systems available, such as falling film, root sprays, or if you are able to inject air into the water to create semi-foamy liquid that circulates throughout the system to prevent root rot.
Most vegetables can be grown hydroponically, vine plants too, heavy foliage plants must be supported with wires hanging from the top, to reduce weight pressure on the system rack.