Well, I've been phasing out my lower-end bags, but not all of the ones I'm keeping are strictly "designer." I never really got into contemporary brands such as Rebecca Minkoff, Tory Burch, etc.--I sort of skipped that step and went right into premium designer bags.
However, I also have one Coach bag (I just adore the style, and it's wonderful for travel), one Cambridge Satchel bag, three no-name gorgeous leather bags I got in Italy, and a handful of interesting or unusual bags from Anthropologie, Furla, Big Buddha, etc. I love interesting clutches, so I've gotten rid of some that I think look too cheap, but I've held onto a lot, too.
I also keep a few bags for bad weather, movies, amusement parks and other places where high-end bags aren't really appropriate.