Originally, I had hoped to do something really interesting with it-- hit 60 by discovering Stormwind, or finally downing Hakkar for the first time. But in the end, I happened to be in the middle of a Scholo run, and it rolled right up on me. Not that it wasn't exciting-- later that night I used all my new stats on a raid and picked up a great mace, and I couldn't wait to get into AV afterwards and finally put the beat down for real. And my experience wasn't as bad as Belle's over in the WoW Ladies livejournal group-- she hit 60 while AFK and offline.
Fortunately, I have another character three levels from 60, so I'm just a week or so away from another chance to make the ding special (I think for this one I'm going to at least try to get my guild to take me to Onyxia for the occasion). Did you try to hit your 60 somewhere specific, or did you just play through until that yellow sparkle showed up for the last time? Or if you haven't reached the holy grail yet, got any plans?