We (Auctomatic W07) applied on a whim back in November 2006. We were in London, had no idea how YC would react to a foreign team, and worse, neither of us could hack back then. I remember discussing with Harj just that week that we really should move to the Valley, but it wasn't really obvious how we should. Harj spent about 10 minutes drafting an application and I spent 30 mins on the train ride home that evening editing it. We had zero expectation that anything would come from it.
We got a call from Jessica that we were admitted for an interview a few days later, and booked a flight for Boston. We were there for less than 24 hours, and I remember Harjeet taking the acceptance call from PG as we were walking through airport security, with the TSA yelling at him "put down your phone! Put down your phone now!". In our excitement, we hadn't arranged a place to stay, or bought a US plug adapter for our laptop for the demo. We woke up extra early that morning to get to Cambridge to buy one, and were early to the interview. (I remember reading that being early was bad, so we did our best to lurk around/stay out of sight til it was our turn).
I distinctly remember the euphoria of being accepted. London back then was a horrible place to run a startup and I ended up writing about the move for the BBC http://news.bbc.co.uk/2/hi/business/6355289.stm (which ended up stirring a lot of debate back in the UK and eventually led to the creation of things like SeedCamp).