To many of you this may seem like a no brainer but I thought I'd share the way I use Twitter's favorite feature anyway because I've found it very valuable over the last few months.
In nearly every Twitter application, and on the site itself, you may favorite a Tweet with minimal effort. On the site you click the star, in Tweetie on Mac I have to secondary-click and select favorite, in Twitterrific on the iPhone I tap the asterisk and tap favorite. Those are the applications I use to interact with Twitter - so your mileage may vary.
Since Twitter is a literal stream of links (Fred Wilson, an investor in Twitter, remarked that its true value was in the act of passing links) I've come across a ton of valuable links from those I follow on Twitter. This can cause a lot of distraction, however. If I followed every single link that I found on Twitter, read them in their entirety, and continued my day ... I do not believe I'd ever accomplish anything.
So that is why I use Twitter's favorite feature to help me save links for reading later.
I still use it to save my favorite Tweets from those I follow. Tweets that are funny, memorable, mark an occasion, or the like - still make it into my favorites list. But mostly I'm using this feature to create a list of things I'd like to read later rather than at the moment they are posted.
This post could stop here because your favorites are easy to access on the site. Whenever you want to catch up on the links posted by those you follow - you could just log into Twitter.com and click on your favorites and do some reading. However I've found it much more efficient to subscribe to the RSS feed of my favorite Tweets and have that fed into Google Reader.
I check Google Reader a few times a week. I fly through my subscriptions and, in general, star the items that I want to read in detail, comment on, write about, or save for some particular purpose. As I'm going through my main subscriptions my favorite Tweets pop up and I'm able to then catalog those links appropriately, with some context, or just star them for later to read.
Not only do I rarely miss a valuable link posted by those I follow on Twitter, I get to read those links when I want to - rather than when they're posted. Value without the distraction.