If you are building a mini-cabinet (4' tall pacman clone maybe?) then using 1/2" or 5/8" MDF can be acceptable for part of the assemblies. I personally would use 5/8" minimum on any cabinet. I would not use it for the base or for support for your monitor and such, but sides, top, back, front can be ok. The load-bearing parts like the base really should be 3/4" plywood.
If you are building a full size cabinet, and have no woodworking experience, use 3/4" materials.
I actually use a lot of different materials for constructing a cabinet. MDF for sides, interior supports and front, plywood or MDO for parts that do the brunt of the heavy lifting. I also use different thicknesses as I feel the need to lighten or strengthen components. Of course I tend to keep scraps and partial sheets from other non-arcade projects, so those get used up in framing a cabinet or whatever else I'm building.