If you don't have Whispernet, you won't have direct access to Wikipedia from your Kindle, as that requires a network connection.
As a consolation prize, you can use Kindlepedia (
http://www.edukindle.com/downloads/kindlepedia/) to convert Wikipedia articles to Kindle format. You have to do that on a PC or Mac, and transfer the converted article via USB.
Obviously, you wouldn't do that if you just wanted to quickly look something up. But it can be useful when you want to read an in-depth article.
One other possibility to get an iPod Touch or iPhone. That has a free applet called Wapedia which gives you access the whole of Wikipedia, formatted for the small screen, from anywhere you have a wireless Internet connection.