But now as an academic living in Chicago I always need to worry about time zones when I coordinate a phone or IM meeting or have a paper deadline. You end up remembering some key rules: One hour to the East Coast, seven hours to Continental Europe except for Portugal which is six hours like London, eight hours to Israel. I always have to remind myself that California is minus two hours not minus three. And of course there is India, currently eleven and a half hours ahead of Chicago. Time zones are relative—your time differences will vary.
Daylight Savings Time adds to the confusion. Europe and Israel have similar time changes but not always changing on the same weekends. India and China don't change their clocks and Down Under they change in the other direction. Savings time also mean extra thinking when converting from UTC time.
Until recently Indiana didn't do savings time but since time zones are relative, it seemed that Indiana changed from Chicago time in the summer to New York time in the winter. Now Indiana follows daylight savings time so most of the state is in New York time year round. I managed to forget the change when visiting South Bend this summer and ended up an hour late to everything.
Technology helps. You don't need to know the time zone when you send email. I used to use the World Clock to keep track of times in other places but now I use the nifty Time in City feature built into Yahoo! Search.
Sometimes time zones can work to your advantage. If you are close to deadline on a paper with a co-author in a far-away land you can each work on the paper while the other one sleeps. This strategy never worked with my most frequent co-author Harry Buhrman in Amsterdam. I am an early riser and he sleeps late so we keep the same hours, seven hours apart.