Speaker grills

Off for listening, makes a difference in the upper end on my Proacs
and because they look much much better (I like to see the speakers, am I the only one?).

On at other times, just for dust protection.

I leave mine on my Verity Fidelio Encores. They take just an ever-so-slight hard edge off the treble.

I think keeping them on render a more neutral sound, sometimes taming a overall to bright amp
using proac studio 140

Grills are constantly on. One pair of speakers cannot be removed, one pair was designed with grilles in place, and the other pair I prefer the look and sound of having the grilles on.
+1 to Mapman’s statement.