As you can see from my backseat, I do. My little Domke bag goes everywhere. Big enough for my DSLR, an extra lens, 2 speedlights, spare memory cards, a Nasty Clamp, and some small odds and ends. That’s all I need for casual walk-around shoots.
For big jobs? Well, that’s what the trunk is for.
Tip: keep a tripod stashed in there.