Speaker grills

Really depends on the speaker like most have already stated. When I had the original DYn C1's they sounded much better without the grills. When I upgraded to the C1 Signatures - well not so much but ever so slightly better without them. Now my Raidho's don't even come with grills.

Remember those thick foam grills on the JBL Century L100's? That type of grill definitely had to go.

Grilles on always. One pair of speakers does not allow removal, one pair specifically designed for grilles on, the other pair I prefer the looks and sound with the grilles in place.
+1 as to what Mapman stated.

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.