I had a bag some years ago that had a little light in it! Franco Sarto made it -- I wonder why we never see those anymore.
I am a big fan of bags that are wider than they are tall -- for me, tall bags are too easy to lose stuff in. Everything just sinks to the bottom, and I have to fish for what I need in the depths of the bag.
I don't like big unwieldy flaps -- I prefer a simple magnetic close, a toggle, or a zipper. Small flaps, like on my red Marc Jacobs bag, are fine. No closures that take more than a second to undo -- no buckles.
These days I want simpler styles. A little hardware or texture, but nothing overdone.
No to bags that have small openings. Deal-breaker right there. No logo-splashed designs.
I don't want a bag that's too soft or too hard. Nothing too stiff or so slouchy that it puddles into a heap if I sit it down.
No to many small pockets and compartments. I'd rather have one or two that I can fit several things in. I don't carry that much these days anyway.
I think all bags should have light linings to make it easy to see what's inside.