I heard the first question the other day and am old enough to have heard the second a while back. Don't get me wrong, I am not saying twitter is the new Internet. It is simply a new tactic to put in our quiver, just like websites, blogs, Facebook and a host of many other Internet applications that have become ubiquitous and, in some cases, effective.
So, should you Twitter or should your company twitter? It would be easy for me to say "it depends" but in this case it really doesn't. The answer is clear, yes.
Without giving one use for Twitter (and there are hundreds), let me explain how I can be so sure of my answer.
Almost ten years ago, when I was working in the Public Affairs Department for State Farm Insurance I remember being briefed by the corporate folks about their desire to have an Internet site and the research they had done to justify their recommendations including: Allstate had one, every day more and more people use the Internet, ability to share information, etc. They were giddy with the thought of our company having a site and, believe it or not, had to fight hard for it. Those for it were the early adopters in the company, the ones with the fancy phones, already had access to Internet at home and loved the whole dancing baby thing. The ones that weren't quite sure about the whole Internet thing... they weren't and were considered by some of us to be a bit out of touch with reality.
Here's the rub, many of those who fought so hard for SF to have a presence on the Internet aren't twittering, they aren't on facebook or anywhere else on the Internet. They could be hiding but I wonder if they haven't fallen off the horse, got behind on technology and just can't seem to catch up. In the interest of full disclosure, there is a State Farm Twitter account, but they haven't yet posted so it isn't clear if they are truly the owners or if they ever plan to tweet.
Move forward to today, should you use twitter? At a personal level, yes, you should. Just like you should have a facebook page, be Linked In, use Youtube and ning, cloud compute, etc. You need to be using them all, and Twitter, to not only maintain your status as an early adopter but maintain your edge and be ready for the next addition/change which, if you follow the trends, are all launched off a previous application (for a kick, map the Internet all the way back to the light and telegraph, an amazing journey to say the least and users of both, way back when, were also considered to be early adopters) so we can be sure, there will be a next step.
How should you use Twitter and should your company use it? Well, we're back to "it depends." How you personally use it is up to you, follow friends, industry (I do both), it doesn't really matter so long as you understand the uses. As for a business use, you first need to answer the question whether it will support a strategy which supports an objective, which supports a goal...My bet, if you think hard, you will find a use for twitter, one that suits your company's needs, just like you found a use for a website and the Internet.
One final thought, when the next app comes out that receives a positive response with regard to the number of users, reread the above and just change out the word Twitter for the new killer app.