There was the time at uni when I clipped a sleeping policeman and was catapulted face-first onto the kerb. Blood, hospital, stitches &c. The irony was that I was on my way to buy gin for the evening's boozing and was, at that time, stone cold sober.
But the absolutely worst drunk biking experience was down Merton St, in Oxford. After Too Much Beer in the Bear, I attempted to cycle down this cobbled st. After about 5 minutes of falling off every 10 yards, I made it to the other end. It's only about 200 yards long.