I built all of my shop cabinets out of MDF and a lot of the painted
built-ins in the house. You could just butt joint or dado them
together, but I recently started using FWW's method which essentially
amounts to a tongue and groove type of construction. My most recent
projects were a 36" high, 20" deep, and 1-54" wide, 1-52" wide MDF
cabinets. The FWW method works extremely well. One thing I started
doing is using a full 3/4" (or I suppose 18MM) thick sheet of MDF as
the backboard of the cabinet and always including at least 1 fixed
shelf (either vertically or horizontally) and securely attaching that
to the backboard. Yields a rock solid cabinet. I don't use any screws
either.