Dunno 'bout where you're at, but every place I've ever been has pointed out that OSHA strongly recommends not re-capping. Here's verbiage from one of their many hand-outs: "Recapping, bending, or removing needles is permissible only if there is no feasible alternative or if such actions are required for a specific medical or dental procedure."
The "correct" (per OSHA) method of handling needles is to use an approved sharps container, which should have a notch for stripping the needle off the syringe and into the container, so that you're never grabbing at the needle, or recapping it, or whatever. (Technically, the "correct" OSHA method is to use needles that are designed to allow safe recapping, but that's not the point here.) Next time you to go throw a needle in a sharps container, look at the container and check out the little notches. I didn't even realize that's what they were for a long time. But then, I'm pretty dim compared to most of you.
The next step down safety-wise is the "recap it on the table" thing where you scoop the cap onto the needle, but I find that just annoying.
But yes, everyone re-caps a needle.