My current travel handbags are:

1) Long enough to put a #10 envelope in it. (so it can fit a folded letter/A4 sized printed e-ticket & other hard copies of my reservations.)
2) Wide enough to hold a small bottle of water plus my usual "makeup" bag that has tissues, lip balm, compact mirror, mints etc
3) Be zippered to keep things from falling out (or crawling in )
4) Be foldable/compressable
5) Be lightweight.
6) Water resistant if travelling during monsoon season.

The bags I have been using for casual trips are the Lesportsac Deluxe Shoulder Satchel , the Lesportsac Deluxe Everyday , the discontinued Kipling Lancelot (back when I was also carrying a 10" netbook in a neoprene sleeve) or even my new LeSportsac Campus Messenger which can hold regular sized magazines a bit snugly. I'm also a fan of the Ellington "Juno" convertible tote-pack. It's the perfect size for a personal bag on the plane, yet the straps can stow away and you're left with a rather nice tote when you need one for places that require you to otherwise check your backpack i.e. museums

For work/something more proper, I have a Longchamp LesPlanetes black Hobo purse. It's just a simple nylon horizontal rectangular tote with a simple black leather trim. It can also hold a #10 envelope and a very small bottle of water/pair of contoured sunglasses.

My mum is fond of handbags that have lobster claw strap hardware so she can wrap it around her waist while dining or going up to the breakfast buffet where she needs both her hands.