I actually had the exact same problem and I was recently speaking to a friend from google and asked him to implement this as part of their search engine (i.e. just like the calculator, but for time zones) -- he didn't see the need for such a thing.
Here is my use case which doesn't work: conference deadlines. Please tell me what this:
Thursday, February 4, 2010, 11:59pm Eastern Standard Time (GMT −5:00)
translates to in my local time. Note that entering the date in your app does nothing, even if you split EST from the rest.
Say you're in PST: put on the right hand side 11:59pm and EST --> 8:59pm that same day.
Say you're in, oh I don't know, Nagoya: same thing on the right hand side --> 1:59pm the next day (the 5th)
I want to think carefully about how to add dates because I'm trying to keep it simple and quick.