My DC1 came 6 weeks early, if that counts? I was admitted with pre-term labour at 33+3 weeks and eventually had him at 34+0 weeks.
Up until about 33 weeks I'd had no inkling at all that he would come early. He was my first baby, so I was expecting him to be late! At 32 and a bit weeks (can't remember!) I had what I thought was a show, then had very,very mild period pains for a few days. But mild to the point where I only noticed them because I was sat down reading a book, I think if I was busy doing something I wouldn't have noticed them. Went for a routine scan at 33+3, mentioned the odd pains, they examined me and found I was 2cm, and the rest is history! Up until that exact point I didn't think he would be early, I'd just put the odd pains down to Braxton-Hicks etc.
Family-wise, I was 2 weeks early and my younger sister was 3 weeks early. Nobody in my mother's family has ever reached their due date. Similarly, my paternal grandmother had both her children early - my dad was 6 weeks early, and his younger sister a few weeks early, nobody seems that sure. Not sure if DH's family history is relevant or not, but he was born at 38 weeks, but ended up being an EMCS due to foetal distress.
I'm now 32+1 weeks with DC2! I've been admitted into hospital twice with threatened pre-term labour, had steroid injections etc at 27 weeks as it looked like he was coming, but things have settled down now. Weirdly I have a funny feeling I'm going to go overdue with this one!