No reservations
Over the years, I've bought a refurb touch, two shuffles, an iPod Classic, and *multiple* nanos. All look new, and come with the same (new) accessories. I have no reservations giving refurbs as gifts. In fact, I only buy refurbished iPods because you can't BTO, so there's no special advantage to buying new, and I don't mind waiting awhile to get a model.
None of the refurbed iPods that I've kept have failed, and I've never gotten a bad report on any that were given. As someone else has mentioned, Apple provides the same warranty and you can add AppleCare for refurbs.
On the other hand, I returned both BTO iMacs for replacements.