The Camelbak-style bite valves, that are the female piece to the male hose, come off pretty easily, and those I do remove.

The Hydrapak-style bite valves, that are the male piece to the female hose, those don't really come off without either loosening the hose so much it won't seal any more, or just cutting it off and shortening the hose. With all the internal hard parts, they're pretty near impossible to clean, too - I wipe them out with Q-tips as best I can and just plan on replacing them when they look too gross.

You can brush the drink tube all the way up to the bite valve even if you can't remove the valve. When I'm drying a hose with the bite valve still attached, I hang it bite valve up, since drainage seems to be more important than evaporation in how quickly it dries, and I just give the valve a squeeze and the whole thing a shake whenever I happen to walk by and think about it.