1). Infant-to-Toddler Rocker by Fisher Price
This chair is perfect if you have a baby and a toddler. If you do, you know that your toddler will want to play with all the toys and equipment that is meant for your new baby. My 2 year old is over 30 lbs and I could just see the destruction she would cause on another chair or bouncer. This chair holds up to 40 lbs. It can be used as a rocker which sits your baby at a good reclining angle or it has a kickstand that lays the chair further back at a great angle for sleeping (at least for the first few months when your baby will sleep in any room anytime.) The vibrating switch allows me to put my baby in there and he stays happy for a few minutes while I take care of my toddler or get dressed. If you don't have a lot of space and can't have 5 different pieces of play equipment this chair is nice because it is versatile and will last into toddler-hood
2.) A Backpack instead of a diaper bag.
I know there are certain people who long for those $200 designer bags. I am not one of them. I need function and practicality. With my first baby I had a black messanger bag. It was adequate but I was frustrated that it would slip off my shoulder while I was lugging my heavy baby around. When I got pregnant with the second one I knew I wanted a backpack. I was lucky enough to get one for christmas while I was still pregnant and that helped a ton because my belly was already in the way and a diaper bag would only take up more needed space around me. I suggest one with two large zipper sections. You can separate things by child or by purpose. I use one side for feeding (nursing cover, burp cloth, snacks/food for my toddler etc) and the other side for diapering (changing pad, diapers, change of clothes for each child, etc). This is also an excellent option if you babywear which will bring me to my next topic.
3.) Baby carriers
If you haven't gotten on this train yet, I highly recommend it. With my first baby I didn't have a carrier. My biceps did all the work as my 8 lb 13 oz newborn turned into a 15 lb 2 month old and a 20 lb 5 month old. I was seriously buff after that first year lugging her around. She was also a needy, gassy baby and was held and carried most of the day. That was hard and I wish I would have had known then what I know now.
I have 2 carriers that are the most useful to me at this point. One is a Ring Sling by Sleeping Baby Productions. Again I did not go for anything fancy just neutral utilitarian and inexpensive though she makes some beautiful slings. This sling is great for carrying in church and around the house, or anywhere that I won't need to be too active for too long. It holds my toddler too, though we've done this more for fun than out of need.
My other go-to carrier is the ERGObaby carrier. I got mine when babysteals.com had them for about 50% off retail. Woo Hoo! I use this at least 4 out of 7 days of the week, much more than my double stroller so far. My baby sleeps in it when we are at the park, library, grocery store etc. Without it I would be stuck at home or would be forced to leave him in his infant seat which weighs almost 10 lbs on its own so carrying him in it is no small feat. If I could afford it I would buy one of these for anyone having a baby. I already want another on in their Sport or Performance version for the warm weather. If you are considering a carrier PLEASE ignore the Bjorn and the Snugli (which hold the baby in a crotch dangling position that can harm their hips and spine) and check out the ERGO.
4) Canon PowerShot S5 IS
Now this is not technically a baby product but is a must have with babies. We purchased this just before my first was born. I was adamant that our other camera was inadequate and we would NEED a new one. This one is not compact but not huge. I keep it in my backpack/diaper bag usually. It runs on AA batteries (which is a bummer but if you get one I would suggest to buy rechargeable batteries). It takes pictures in almost any light very quickly (great for catching those cute faces and action shots.) It also has a high quality video recorder so I can switch quickly between photos and videos if my kids do something brilliant that needs to be filmed. There are probably newer versions and I would love an even better camera with the same features but one thing I try to tell my friends having kids it to get a camera that takes pictures quickly and takes them indoors well. If you aren't worried about a little bulk for better pictures get a camera like this. :o)
I will add more products I have found useful as time allows so stay tuned. :o)