The internet is all a-chortle with reports of Kindle Fire owners having trouble connecting to those self same internets. Amazon's own forum is full of people who can't connect to Wi-Fi, or can connect to Wi-Fi but not their network.
It's not entirely clear what the issue is and Amazon hasn't acknowledged the problem in any official way, but the good news is that it sounds like there may be a fix. The majority of those who are reporting connectivity problems are using version version 6.1 (or occasionally 6.0) of the OS. If you can't get online at all, download version 6.2 on your computer and load it onto your Fire via USB, it sounds like that's solved the problem for a lot of people.
It's possible to assume that the Kindle Fire has a less tech-savvy user base, which could result in more user error than usual, but that this appears to be a legit bug, and our own resident Linux god Chris Beidelman has confirmed it on his own machine. Have you had Wi-Fi problems with your Kindle Fire? Let us know in the comments, and please include whether or not upgrading to 6.2 helps or not.
(Side note: The Kindle Fire is a new thing with a new OS. So why start their OS at version 6.0? Who do you think you're fooling, Amazon?) [CNET]