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Twitter does not have a tagline, nor does Digg, Blogger, Technorati, Craigslist (if you consider it a web 2.0) et many others.
On the other hand, some web 2.0 services have built their identities leveraging tag-lines and often changing many overtime.
Facebook is a good example - here is its tag-line history:
“Keep up with friends and family,” “Share photos and videos,” “Control privacy online,” and “Reconnect with old classmates.” Now Facebook has a simple message to entice you to sign up: “Facebook helps you connect and share with the people in your life.”
Is Facebook managing its tag-line reactively or proactively? In other words, is Facebook reacting to the users' behavior, so to hone the potential of its brand - or - on the contrary, has Facebook elected to pursue a specific marketing strategy, irrespective to its users?
I understand that, once you have reached the dimension of Facebook, such question become a chicken and egg question... However, I am keen to believe that the importance of auto-determination of an online community is expected to impact the use of tag-lines (or - at least - the evolution of the same).
Some other examples - Youtube "Broadcast Yourself", and Myspace "a place for friends".
Now, empirical evidence shows that only a minor percentage of Youtube users is actually uploading videos representing themselves, while the majority of the users is just "watching-someone-else." Most of the users would rather mirror themselves in a tag-line such as: "find-here-the-TVshows-of-the-80s-you-used-to-love-so-much," or also "show-your-friend-a funny-video"... Of course, these are not quite the actual lines to have under a logo... but I mean the content-message of these tag-lines is closer to the community than "broadcast yourself", even though I concede this last one sounds very nice...
Now, I believe you are ready to try this exercise on your own, with Myspace "a place for friends". (Friends? Sure...)
If you are curious to read more tag-lines click here.