I'm not an expert on babies or baby stuff. But I've strolled around the block with 2 babies now, and have learned a lot of things and tried a lot of things. I've used many things that do not work, but here are a few of my favorite baby products that do:
The Booger Sucker:
The booger sucker *ahem, excuse me* nasal aspirator that we got from the hospital is a piece of junk. It is too stiff and just plain doesn't, ummm, aspirate. This handy little sucker from Little Noses works much better. It even has a clear tip so you can see the snot going in and have an idea of how much you got! Awesome, right?
The Nuk/lovey combo:

This little guy is a
Wubbanub - it is a Soothie pacifier with a stuffed toy attached. We have had this monkey one since Linus was born (thanks, Laurie!), and the other ones are super cute too. If you do a nuk in the hospital (we didn't with Felicity, but did with Linus), they will probably give you a Soothie. I don't know how Soothies got to be the "hospital approved" pacifier, but lucky them. :) If your baby likes that kind, you can try a Wubbanub. The best thing about it is that it doesn't get lost! Ok, that's not true, a kid can certainly lose it along with your keys, cell phone and important mail. But it is way harder to lose than a tiny pacifier with no toy attached. It doesn't fall through the crib slats or roll under the bed when you drop it. It also helps with the "baby-wants-pacifier-but-keeps-spitting-it-out" problem. The weight of the toy helps it stay in place when you prop it next to the baby or lay it on his tummy. He spits it out, but if it doesn't go anywhere, he can get it back into his mouth. And it's fun to grab and hold - a soother and a friend all in one.
Un-Medicine:

Homeopathy is something I don't know a lot about, but someday want to learn. I would much rather heal my body with extracts from plants than chemical drugs (though we use them when needed, of course). The company
Hyland's makes a number of homeopathic remedies for all ages, and I love their products. The first one we tried is pictured here - teething tablets. When Felicity was 8 months old, we spent a very miserable night comforting while she cried and cried - very unlike her. The next day, I felt her gums, and there was a tiny sharp spot! I was advised to go get these "amazing" tablets, and had them ready that night. When she woke up, I nursed her but she started really crying again. We melted 3 of these in her mouth, and ten minutes later she was asleep. Yep - amazing! The bottle actually warns you not to be alarmed if your baby falls asleep after taking these (you might think they were drugged); it's just that the pain is gone, and now the baby can sleep again. I have also tried the Cold 'n Cough 4kids and the new Baby Cough Syrup (last night actually - poor Linus) with excellent results. I'm not a fan of masking symptoms like fevers and coughs; they are useful to the body. But if the fever is too high, or the cough means no one can sleep, ya gotta do something.
Hands-free Baby:

This is my awesome
babywearing husband with our 1 week old Linus in the
Moby Wrap. It is my favorite baby carrier because it is the most comfortable to wear. It's not as great for bigger babies, but I can't wear a heavy baby in a sling for long anyway. Jeff has spent hours with our new babies in a sling while he gets other stuff done (computer-type stuff, not using a saw or anything :), and I love being able to hold my newborn without tiring out my arms. Babywearing is great for keeping babies soothed and happy, for letting them look around, and for snuggling them (similar to swaddling) for good sleep. Babies love it because it's about as close to the womb as they can get since leaving that warm, cozy, rocking place. I should qualify this and say "most babies love it." Babies are individuals too, and some will hate slings, swings, strollers, nuks, being swaddled, and anything else someone tells you to try saying, "This
will soothe her!" Other carriers we have loved include Ergo and Kanagroo Korner, but I'd pick the Moby if I could only have one.
Real Diapers:

I want to talk about cloth diapers, but really explaining them requires a whole separate post. They are a little more work because you have to clean them, but I really love using them. Cloth diapers contain messes pretty well (just think, would you rather wipe up a mess with a paper towel or a thick rag?), save you tons of money, keep trash out of landfills and are not full of chemicals. Friends occasionally ask me what kinds I use/like, so I will write on that sometime soon.