Like with most others, only when it needs replacing.
Occasionally I might buy a couple of new wine glasses or something, if I think they're pretty and will make my life better (lol), but I can't really afford to be replacing things often, even if they look a bit tatty.
We bought a new washing machine last year, but the old one broke. We probably could have had it fixed, but our new one is more energy efficient etc. I'd like a new fridge/freezer, but the old one still works, it's just in a state. So I won't get one.
I really need new carpeting/flooring in the living room/dining room – it's old, threadbare, and incredibly stained and nasty. We can't afford it though, so we just don't bend down and lick it anymore.
Bedding – this is the area I've been known to be less frugal with, because I get bored easily of certain ones. I'm currently trying very very hard not to give in and buy a new set, when I've got several perfectly good ones at the moment.