Ok-I'm not exactly sure if I remember this correctly but I believe if you create a baby registry on target.com that they will send you a card to bring in store with a copy of your registry and you should be able to get a $20.00 gift card from them. I used it to put towards my diaper bag which originally cost $50!
Also, I check samplestuff.com daily & there are occasionally baby related items either coupons/discounts/sometimes free samples too. Coupons.com has tons of great coupons (not free but sometimes they will have like $2.00 of pampers/huggies etc. which isn't too bad).
I signed up for the 3 month trial of Amazon Mom awhile back-2 day free shipping & 'prime eligible' discounts which are pretty nice. I actually ended up signing up for the annual pass after my trial was up. Costs $79/yr. but you get the 2-day shipping, free movies (similar to netflix as long as they are 'prime eligible' & if you have a kindle one free book/mo.)
What PP have said about Enfamil/Similac are really the only free samples guaranteed to be geared towards babies that I can think of. But if you ever do a lot of online ordering-I use ebates.com to get some cash back from purchases made online (they will mail you a check every 3 months, I order a ton online so this is very useful for me) Retailmenot.com you can usually find out who is having discount codes & they have printable coupons as well.
Hopefully this was somewhat helpful!