I must be really lucky because I can't think of anything that we bought for bub that hasn't turned out to be useful, but here are the top lifesavers:

1) Towels - all varying sizes - Large towels for drying bub after a bath, wrapping bub in (instead of a wrap - so much easier to wipe any dribble or vomit), putting down on the floor to give bub tummy time. Medium towels (or cloth nappies) to lay in bassinette or underneath wherever you're putting bub down (once again, to catch any dribble, vomit, wee, etc and not have to change the sheets). Small towels (I bought a bunch of facecloths) to keep in your nappy bag or handbag and in handy places around the house for any accidents.
2) Sling to carry newborn bub around.
3) Baby Bjorn to carry older bub around.
4) Nappy sacks - so cheap and they really do neutralise the smell of nappies.

Things that are not so useful (fortunately we didn't actually pay for any of these, he he):
1) Nappy bag - we got given a cool looking designer one, and I do use it, but if no one had given it to me, I would have just put all the nappy stuff in one of those cloth green bags - so much easier to access everything you need and a much better size.
2) Change table - our one sits in the oorner of the room. We use the shelves for storage, but change bub on a changing mat on the floor.