Hmm...
I have some very strange and outlandish methods that will seem surprising:
1) I use an Indian brand of "chinese chalk" called "Lakshmanrekha" (insect repellent) and draw a border at the base of both speakers. I also lightly coat the speaker cable in this so as to prevent ants, etc. from climbing onto it. It has worked well for me. I also draw a border around the rear ports to prevent insects from entering it.
2) For the drivers themselves I use a Scratch-Proof wipe from 3m/Scoth-brite. This is a micro-fibre cloth that I hope is safe on such delicate parts.
3) For hard to reach places such as rubber surrounds I use a camel-hair brush but very lightly. Obviously the brush is used only for this purpose.
4) I use a sticky "lint roller" for the cloth grills.
5) Soft cloth for rest of the speakers, i.e. sides, top.
6) I keep naphthalene balls near the speakers and the equipment.
7) Silica Gel bags near amp & players.
Would like to hear what other members are doing.