I usually remove the monitor chassis and neck board. Spray them with simple green, let sit for about 5 minutes then hose it off. I use canned air to knock the majority of the water off, then let it sit for a day or two inside.
For the tubes it depends on how dirty they are. Sometimes I just brush the crud off with a soft bristle brush and canned air. For really dirty ones I'll spray them as well, but try to keep the spray confined to the yoke and neck area. I'll take a damp paper towel and gently do the area with aquadag by hand.
I also use simple green and water on game PCB's if they're bad.
Apart from the dirt acting as an insulator causing components to lose some cooling ability, there's nothing like pulling a clean chassis out to do a cap kit compared to getting your hands all black with years of filth. Not to mention trying to keep your solder joints clean when there's dirt all over.