If the laptop meets your requirements (in terms of speed, disk capacity, etc), there's no reason not to buy it. I've got a laptop that I paid £60 for at auction, where a dealer regularly offers such refurbished laptops for sale.
The only things to watch out for are battery life and software (and, in particular, the operating system). I was unsurprised that the battery in my cheap laptop was all but dead (but I only ever intended to power it via the mains adapter anyway) but it came with a clean installation of Windows XP and some basic software pre-loaded.
So check that there's a new battery (or, at least, a good quality one) in any refurbished laptop and, of course, that it's actually got an operating system on it. (The price will rocket if you have to buy Windows as well!). XP is fine for most purposes but Vista (although more recent) is probably to be avoided.
I doubt that Amazon, per se, actually sells secondhand laptops. The sale will also certainly be offered by a third party (using 'Amazon Marketplace'). Look for the name of that dealer in the ad and then google it together with the word 'review'. That might help you find out if that dealer's products can be trusted.
The refurbished laptops here are dearer but I can thoroughly recommend this company to you:
http://www.accomputerwarehouse.com/products/computing/laptops-notebooks/refurbished
Chris