During all my years riding in NYC, I kept a spare tube strapped to the underside of the saddle with a toe clip strap and it never got jacked. I wouldn't leave valuable tools on the rig, but the tube itself seemed to have no appeal to the criminal element. As for patching vs. replacing, I join the rev: replacing is quicker, and you can save the busted tube for a subsequent patch job. Anyway, sometimes it's too hard to find the puncture on the street - if it's dark out, you can't see it, and if it's noisy you can't hear it, and if it's windy, you can't feel it.