You can stash the quotes you come across in a big, tagged tool like Evernote, but some people prefer focused, purposed tools. Quotabl.es is such a web app, providing a bookmarklet that captures inspiring quotes anywhere on the web.
Head to Quotabl.es, create an account, and grab the bookmarklet. Highlight any text you like on a page, then hit the Quotables link, and you'll get it nearly squared away, after you choose the author (which is often auto-completed, and sometimes filled in, if you copied more than just the quote). You can further tag and categorise your quote, and choose whether it stays private or goes public. Quotables itself is getting filled out nicely with great quotes from all over the spectrum. If you dig the occasional mind-moving quote, as we do, Quotables seems like the right place to keep them together.