With Firefox 3, you can easily select multiple and non-consecutive pieces of text from a web page as shown in this GIF screencast.
The secret is the Ctrl key. Select a line in Firefox with your mouse and then press the Ctrl key before selecting the second line.
Unlike other browsers like IE or Opera, Firefox will not clear your previous text selections if the Control key remains pressed at the time of selection. This feature will definitely come handy while clipping web pages. Thanks Keith.
For some reason, the trick did not work for me on Google Search pages and Google News but I guess the culprit is Firebug.