There are many ways to save paper while browsing the web including choosing the printer-friendly version, setting the range of pages to print, and printing only the selection. Another method is to remove any unnecessary elements from the page before printing, such as large banner ads. The Firefox extension Nuke Anything Enhanced is one of the most versatile tools for trimming a webpage for printing.
For example, at the top right, we see the article on CNN.com about Princeton's ZebraNet project, formatted for printing. Unfortunately, the printer-friendly version of this article still has a big ad and other unnecessary text. By selecting parts of the article and using Nuke Anything Enhanced's “Remove selection” and “Remove everything else” operations (left, and below), we can trim down the article so that it is just the parts we want (bottommost).
Other Firefox extensions which provide similar functionality include Aardvark and Platypus. Even if you don't use Firefox, there is tool called Click2Zap, which runs on most web browsers (special Internet Explorer version). The author of Click2Zap has created a second tool with greater control called MyPage. Finally, if you want to make this process happen automatically, you can use AdBlock Plus to prevent almost all internet ads from appearing on your computer.
If webpages worked like a newspaper or magazine, you could cut out and save arbitrary clippings, such as an article, a picture, or even just an important paragraph. If you are using Windows, the HP Smart Web Printing tool is designed to do exactly that. It lets you make arbitrary selections for (multiple) webpages and integrate them into a single scrapbook-like document for either direct printing or conversion to a PDF.