I packed mine at 32 weeks as I was bored! I have a bag for me for labour, a bag for baby and an overnight bag as well as I'm being induced at 38 weeks and I might need to stay in a few days.
A good tip that I got from here was to put a little draw string bag in your labour bag with 1x nappy, 1x vest, 1x sleepsuit, 1 x hat and 1x scratch mitts, that way you can get LO dressed right away and not have to worry about taking baby bag in as well as labour bag. We are going to leave it in the car and DH can get it later on so we can bond with baby straight away.