I was packing my bags last night ready to fly out of Phuket, when I took a second look at my passport and realized that I had overstayed by visa by one day. I had arrived in Thailand on May 16th, and made the assumption that my visa was expiring on June 16th - daft assumption, but I am sure that in previous countries this system worked!
I searched the TA site to see what might happen and got a mix of results.
For your information - my experience flying out of Phuket in June 2012 was that when I walked up to the immigration counter, the official looked through my passport, simply said "500 baht", and pointed to the little 'overstay' office behind him. I went in there, paid my 500 (looking meek and apologetic), and that was that - money was taken, passport was stamped, and there is also some sort of note written against my visa stamp.
This is clearly a common error and nothing to panic about. On this day at least, there was no 'waiver' or 'one-day pass' as some suggest (maybe this happens more in Bangkok, where the tourist traffic is huge), but it wasn't a biggie either.
If you have just realized that you have made the same mistake, and are searching TA for answers, I suggest you don't worry too much -they are likely interested in the 'real' overstayers who have been there much longer, and in any other 'dodgies'.
I would note though that the common theme in these forums is that even if you have overstayed by only one day you should try to avoid contact with the police at all costs - there's apparently a 'law' that they are required to report any overstay. I am sure there are plenty of expats who would tell tales otherwise, but there you go.