Refurbished laptops from Apple and Hewlett-Packard are relatively inexpensive and, in many cases, virtually new. But it all depends on how you define "new."
Let me begin by saying that I would not recommend a refurbished laptop. That's just my experience, of course. I recognize that others have had positive experiences and that some would swear it's like buying a new computer, just cheaper. But I have purchased two refurbished laptops--one from Apple, another from HP--that were both defective out of the box.

Apple case first. I recently purchased a refurbished Apple MacBook Air. Unpacking it revealed a pristine, brand-new looking MBA. Until I turned it on. The screen was dimmer than the screen on a one-year-old Air I have been using and the backlighting was uneven. In short, the bottom 25 percent (roughly) of the screen was noticeably darker than other 75 percent of the screen.
Moreover, upon closer inspection I could see that the screen had rather prominent dark blotchy areas (more prominent than the "normal" blotching you get on these screens). Ironically, the much older Air did not exhibit this. Now, I realize that I may not have considered the screen defective if this had been my first Air and I hadn't been using another MBA (which, by the way, I had intended to pass on to someone else) that had a gorgeous, uniformly backlit screen. But nobody, I would submit, likes trading down from something great to something less than that.
And what is the single biggest difference (aside from specifications) between the two Airs? The non-defective, problem-free one was purchased new.
I have a lot of scary, unpleasant theories about refurbs--none of which could ever be proven unless I actually worked at a PC manufacturer--but I think I can safely say this much: some refurbs are less than meets the eye. They may look pristine on the outside but mask internal problems.
Which brings us to my HP business laptop refurb. This is a much longer story that I will summarize briefly as follows: out of the box, the keyboard was defective and the unit randomly shut down (that latter problem, I concluded, was due to overheating). I had to go through a pretty painstaking series of steps to get both of these problems resolved.
The moral of the story may be this: you get what you pay for. A buyer of a refurbished HP business laptop can save a lot of money--sometimes more than 50 percent off the list price of a new unit. The cost savings on a refurbished MacBook that is still being actively marketed by Apple is less: in the case of the Air, a few hundred dollars.
So, what is a refurbished laptop? Here's what HP says on its FAQ page:
"Stringent guidelines are followed. All units are brought up to fully functional condition, with defective parts replaced by working parts...Refurbished business products go through two quality control checks before being re-boxed for sale to ensure high reliability."
I'm sure both companies strive to offer just-like-new refurbished laptops but my experience is that refurbs may be more trouble than they're worth. I would like to hear the experiences readers have had.