It's not quite inevitable but very common.. definitely not 1 in 4 as someone else said. However, you probably won't even know or care at the time!
I remember someone posting a link to a labour and delivery nurses blog entry on this worry and this quote from her pretty much sums it up "As a labor & delivery nurse, I do not keep records of exactly how many women poop during birth (can you imagine pooping statistics! haha! J) but you can rest assured that it is the VAST MAJORITY of women. If someone you know tells you they didnt poop during childbirth they either are: #1) part of the very small minority of women who actually dont, or #2) just didnt realize they did. And to be honest, #2 is way more likely!"
xx
I'm not sure about that. I KNOW I didn't poo with any of my three births - it can't be such a small minority if it has happened to me three times.
I think a lot of it has to do with how long you push for.
I pushed for 6 minutes, 5 minutes and less than 2 minutes with my children. If I had been pushing for an hour +, things may have been different.