I always make the best casual shots when I have one body, one lens.
Any more than that and it becomes too much of a chore.
When I just have one lens, I spend my time thinking about how to make a great photo, rather than what lens I want to switch to.
One body, one lens. Set out with a goal in mind, and your photos will be better for it. Pick whatever it is that is suited to that task.
When I go out to shoot architecture, I'm prepared for that - and I don't get upset if I miss a great landscape opportunity, because that wasn't the goal of my outing.
Aimless wandering is useless.
Yes, even when traveling I stick to these ideas.
There is a caveat however - if you know what you need to get the shot that you have in mind, feel free to take the lenses (plural) or bodies that you know you will need. A sports shooter, for instance, might have a 70-200 on one body and a 400 on the other, but he isn't wasting time deciding what to use because he knows how to get the shots he has in mind. He's using the bare minimum and his shots are better for it.
edit: that's what i get for grunching. didn't read bohdank's post, but he is saying the same thing that i am.