The Kindle is a device optimized for reading, so if you're looking for lots of snazzy video game stuff it's not the toy for you.
That said, Hasbro Electronic Arts has created a really nice Scrabble game application for the Kindle that works exceptionally well. So far I've only played it solitaire against the built-in AI, but the game does have the option for playing with up to four other people in a sort of "hot seat" mode (I assume you'd just pass it around.)
The AI at "Normal" level isn't too hard to beat. It knows a lot of strange words, but it doesn't play very strategically. I found it's style to be a very frustrating defensive style that seems most interested in blocking YOUR moves rather than trying to set itself up for high-scoring plays of its own. I have found that this makes it vulnerable to a steady counter play that concentrates on scoring moderately well every turn (10-15 points) rather than looking for Bingos or other big plays.
It plays using all the usual standard Scrabble rules.
The interface is very easy to use, and is based off the "5-way" controller on the Kindle, making it pretty intuitive. My only concern is whether the 5-way is designed to take that much use over the long haul. Normally, while reading, you don't use it all that much.
Still, it works well so far and the price is very affordable, just $4.99, making it just about the least expensive Scrabble game available. Overall I like it and I think it's almost a "must-have" for a Kindle owner.