I should preface by saying that I have never had the means to purchase a very high quality bag, like a Coach. But I do have a ton of bags, a whole closet-full to be honest. And I can safely say that my favourite brand, judging by the number of them I have, is Nine West. Its an affordable brand that I always seem to like their designs, and the bags have held up REALLY well over the last 10 to 15 years. I pull them out from time to time to change bags, and almost always get complimented on my old Nine West bags. Voila!

Going in price order, bags I've owned/still own and really enjoy.
Louis Vuitton (once they break in, my favorite bag)
Coach, Kate Spade, Dooney and Bourke (but not outlet versions, then the leather is too thin)
Fossil, Lucky Brand (they wear like iron)

I'm with Gaylene when it comes to Matt and Nat...I have several of their bags (older styles) which I love.

Another vegan company I discovered last year was Pixie Mood. They are Canadian and vegan. A lovely friend gifted me this Pixie Mood bag:

I don't have a favorite brand, but am on the lookout for a new bag! My current favorite handbag is MK, but I won't buy another MK bag. Here, everyone has a Coach or MK, many are knockoffs (why? the real ones are pretty affordable), many wearers are teens. I don't want to be lumped in with that demographic, so I won't buy those two brands.

I tend to like D&B and Cole Haan bags. I always cruise through the bag section at Nordstrom and Nordstrom Rack in case something catches my eye, in any brand.