I may be a bit late to the party but I was finally able to see the power of Twitter this afternoon.
I kept on getting an "Authentication failed" message when trying to log in to AIM. A few years ago I would not know what to do except ask my friends if they were having any trouble. Right now, I went to searched for "AIM" on Twitter and discovered that other people were having the same problem. Turns out it was a systematic problem and I wasn't the only one affected. Being able to know more about this problem is a great benefit. There has been a lot of talk of the power of real time search and real time news but this was my first real glimpse into the power of Twitter.
My first action wasn't to search for "AIM log in problem" on Google but to search for "AIM" on Twitter. It's amazing to me that Twitter was able to replace a certain type of search. The majority of my searches will still be done on Google but it seems that for anything with a pulse - Twitter search is the way to go.
Twitter's character limit is a great way to take advantage of the network effect. Having a low character limit encourages a lot more users to tweet thereby making Twitter feel alive and giving everyone else more information.
There have been numerous ideas of Twitter being used for market research and to get an early customer response - I can imagine that happening now and it's mind blowing.