I replace mine daily - or, if I've done a particularly greasy/yucky sink of dishes, a couple of times a day. I knit and crochet them, MIL knits them for me, so I have plenty to use.
I drape them over the sink handle when not in use, and once they are dirty, I have a dedicated small dishcloth hamper in my kitchen.
I get squicked out by washing things for my dishes in the same load as things for my bum, so...separate loads it is