I do but only under certain conditions. I will take the dogs with me on errands if it is not too hot or cold out and only if I'm going to be in the store for under 20ish minutes.
If I go somewhere where my dogs can be seen from the store (like a window seat in a dinner or the like) I will still bring them even if I will be a little longer because I would be able to see them.

You'd be surprised at the amount of stores & the such my dogs can go into though. So they come with me more often than a lot of people would think. A few of my friends own stores & allow my dogs inside, a lot of my shopping is done at pet stores & they are welcome there too, my friend who owns her own hair salon allows my dogs there when I go, my dogs are allowed in a few bars too (obviously I only allow them to come when it's not busy and even then I rarely go anyways). Pretty much the only time I have to leave them at home is when I go grocery shopping.

I lock my car & turn on the alarm and if Raustyk is with me I still lock & alarm my car but you would have to be really stupid & have a LOT of guts to mess with my car with her in it... you'll know why before you even get near my car. She is VERY protective of my vehicles.