Thermometer - Those thermometers that scan the forehead and the ones you stick inside the ear are pretty cool, huh? Well, your pediatrician won't be very interested in what they have to say because they're not accurate on babies. Get two regular digital thermometers. Then get our your Sharpie and label the first one O/A (Oral/Armpit). This is the one that you'll stick under Baby's arm. It's not entirely accurate, but add a degree to what it tells you, and you'll get an idea of whether or not Baby is running a fever and whether you should proceed to the second thermometer, which you're going to label R. R stands for Rectal, and I know that probably freaks you out. But after the first time, it's not a big deal, and it's the most accurate way to get a baby's temperature.
Nasal Bulb - Don't buy one. The one the hospital gives you is perfectly fine.
Baby Nail Clippers - Get something simple - no magnifying lenses and no lights. It's hard enough to see what you're doing without the extra stuff getting in the way (even if it claims to help you see what you're doing). Since most of the parents I know have a story about cutting off the tip of their baby's finger (I'm so serious), put them away for as long as you can. Baby fingernails are so thin that they can be bitten and/or peeled off for a good long while.
Infant Acetaminophen Drops (a.k.a. Tylenol) - The dosing for tiny ones isn't on the box, so ask your pediatrician at your first visit so you'll know for future reference.
Infant Ibuprofen Drops (a.k.a. Motrin) - Ibuprofen is better for teething pain because it's an anti-inflammatory
Mylicon - These are anti-gas drops that some people swear by and some people think are worthless. You'll never know unless you try, and if you have a colicky baby, you'll TRY. ANYTHING.
Gripe Water - This is another remedy that works for some and does nothing for others. It seemed to help our kids. I've also heard of some brands working better for some babies than other brands. If this is the case, you might have to experiment.
Probiotic Drops - These are expensive, so hold off unless you actually have a colicky baby. We tried them without success, but they do help a lot of babies.
Baby Saline - When Baby has a cold, the saline helps loosen up the snot so that it's easier to suction out. Also useful for the dry indoor heating of winter.
Humidifier - A humidifier works wonder for a baby with a cold. Again, also useful for winter dryness.
Dandruff Shampoo - Huh? For a baby? I wouldn't actually put this on the registry, but just be aware of it. Chances are that your baby will have cradle cap at some point (both of mine did), which will make your baby resemble the weird, flaky kid who sat in front of you in 9th grade. I found dandruff shampoo to be effective at holding it at bay. For when it gets really bad, you can slather baby's head in olive oil, massage, and then slough the flaky chunks off with a comb.
Comb - I wouldn't even bother with a brush.