Searching and Wikipedia are a big deal
I think two of the biggest features the Kindle has over many similar devices are full-text search and the ability to do lookups to Wikipedia (and similar datasources).
Search is not entirely new, but not all competing devices support it and the Kindle's keyboard makes it a bit more convenient.
I often find myself thinking of passages I read in the past in some book and want to find them for reference. This is obviously a pain in a paper book which lacks any sort of search mechanism. With the Kindle I can do a quick full-text search and even clip out the passage I want and export it. This was not possible on my Sony 500.
The ability to temporarily sidetrack into Wikipedia (or some other reference work) is also a major change to the way I read. In the middle of reading a book or article you can bring up Wikipedia and read about a topic, then resume reading at the same place.
Currently you have to type in your search terms using the search button and the keyboard. It would be nice to be able to point to a line of text and then get a popup window of the words in that line and pick one to search on. You can do this now but only for a quick lookup of the built-in dictionary which is usually pretty useless, as it tends to only show you definitions for the easy words and quietly omits things it doesn't know. Also it does a really bad job in some cases such as the word "called" bringing up "CAL - Computer Aided Learning" as a definition. Clearly the computer could do with a little more learning of its own.
Anyway, both search and lookup are features which go beyond replicating the paper-book experience and are likely to change the way we read.