I quit carrying a purse in 2003 when I lived overseas. I was out in the local areas quite a lot, I didn't want to look like a good person to mug. I streamlined my daily baggage to my driver's license and debit card in my back pocket, then some cash in a front pocket. For a while I carried it in a little wallet, but eventually I decided even that was unnecessary and I just put the cards themselves in my pocket. Besides, the little wallet gave me a lumpy butt!

(Warning: this can bend/damage your cards if you have a "curvaceous" caboose like I do... lol). I still manage my daily baggage this way. Today when I leave for work, I will have in my pocket my drivers license and my debit card, and a little cash. I know I won't need anything more than that today. I will also have a lip gloss in my lab jacket, but I don't really know why that is necessary because I have lipstick and lip liner in my locker at work... but whatever. I suppose it's just something to slime onto my lips when I'm in a hurry.
I still kept my bag around tho. I have a small black leather backpack that I picked up in Mexico 5 or so years ago. I love it, it cost me $20 and it has been the handiest thing. It became my "dance bag" (not to be confused with the "shoe bag"). I kept the dance necessities in my dance bag: change of shirt, perfume, hankerchief, fan, breathmints, microfiber cloth (for smudges on my glasses - it happens and is *way* annoying!), ...assorted other stuff that others have already listed...., yadda yadda.....
I also have another brown handbag that I keep around just in case I'm wearing brown shoes, but that rarely happens anymore. Both the brown handbag and the black backpack were selected because they were the right size to carry a diaper (just one!) and a small package of wipes - I had babies when I bought them. But the babies are grown enough that I don't need to carry diapers with me anymore, so I don't need to carry all that crap anymore either. HOORAY!
I do have an adorable evening bag that I picked up overseas that looks like a chinese take-out box. It's covered in satin-embroidered-with-dragonflies, and the handles are chopsticks. The problem? I've become so accustomed to not carrying a handbag that I feel awkward when I use it, or I forget it completely. One of these days.....