This tip will work for any vent; I used this on our air intake vent (the most shockingly dirty vent in the house).

Below, my 2/3 cleaned vent is nice and white on the left side, and disturbingly grungy on the right side.  I am convinced that you cannot appreciate the actual level of grime by looking at the picture.  Believe me, it was obvious to anyone walking by.

So, how do you clean a vent without taking the whole grill off?  My dear neighbor, who cleaned professionally at one point, taught me this trick.

First, gather cleaner of choice, a metal butter knife, and a cleaning rag.

Second, wrap the cleaning rag around the knife- if it is a thin rag, double the layer.

Third, spray the vent with cleaner (whatever you’re comfortable with, be it 409, or an eco-friendly non-toxic cleaner, or just water. Seriously, whatever floats your boat.) and insert knife between the metal slats.  Clean side to side.

Fourth, readjust the rag as necessary so you have a clean area of the rag to use.  Rinse and repeat.

Et voila, after less than five minutes: a vent that is spic and span!

This is a particularly good trick for vents that are very difficult to remove, or the paint would be damaged by removing.