Well, my first "real" app in my mind was an international clock for Mac OS X. This was back when OS X was brand new and wasn't even the standard operating system on Macs, so I really didn't have any good existing options. I had a lot of friends in different time zones and I had trouble keeping track of who was likely to be available at a given time, so I made an overlay dashboard that I could glance at to see what time it was in whose area.
I'd made a bunch of little games and DHTMLy web pages before that, but that was the first one I thought of as an app I'd made.