When I was packing our bags for DS2 I think I put in about 5 little outfits. I knew I'd be in for at least 4 or more nights (turned out to be 6 nights as he was born a month early, and I had a caesarean too) so figured I'd start with 5 and if I ran out DH would be able to bring dirty clothes home for mum to wash and bring clean ones back. I usually only changed their clothes once a day, unless they got awfully dirty with vomit/poo as has been pointed out. My DS2 actually spent some time in SCN so they provided clothes for the first few days anyway - I actually found both times around my boys were automatically dressed by the midwives in hopsital clothes to begin with as I was a caesar patient so they did it all for me. All hospitals are different though.

Good luck!