Other than watercolor, which I hardly ever use, my brushes get pretty grungy. I'm not the greatest at taking care of my brushes so when I have to clean them- I really have to clean them.
I found a silicone oven grip at a yard sale last year that I've been using to clean my brushes (works great for makeup brushes too). It's just soft enough, yet textured enough that I can really scrub my brushes against.
It's reusable, easy to clean and dries quickly.
Use a mild dish soap or even a facial cleanser for your brushes. If your bristles get too dry, scrub them in some hair conditioner to retain softness.
The textured grips also make great stamping platforms (: