I don't know it depends. Sometimes I might keep a case on for a day or two. My otter box defender and my book book usually stays on the longest out of all of them. Sometimes I use no case for a while too.
Longest I've lasted in the same case is probably 5 days. I get VERY bored! Probably the reason I have around 15 cases :-/ have to say I've been slowing down. Probably will only get a couple more summer colors I've been eyeing. I usually last 2 or 3 days typically.
I find a case a use it daily until I hear about another one I'd like to try. Currently, as I'm moving more toward a minimalist approach without going nude, I'm using my Elago S4 Slim Fit in white. Can't see a reason to take that off.
I have 2 cases right now - an OtterBox Defender and a PixelSkin HD (Speck). I love the PixelSkin, but it's pretty grimy now. I just picked up 2 candy shells on Amazon and the incipio stowaway case to use on vacation (and any other times I don't need to carry my wallet).
I leave my OtterBox Defender on full time. I take it off every 2 weeks for deep cleaning with some monster iKleen solution, microfiber cloth, and q-tips. I am looking at grabbing a life proof to switch between the two.
I use to change mine weekly (how sad is that? and, when I wasn't changing cases, I was browsing for cases online... lol) ... but, now I I'm pretty much sticking with the personalized Otterbox that I got from lipstickshades online.