I have found an great way, depending on the type of cabinet and what you have in it.
I have built 3 mame machines using old, stripped taito cabinets that have the original monitor mounting plate in them. Using a 20" or 21" monitor (both will work), I removed the entire back plastic cover. The monitor then fits perfectly into the monitor mounting plate and the monitor is then held in by gravity by the front plastic cover.
Just like eightbit, this easily slides in and out of the cabinet and can be taken out when I want to move it.