Honestly, Toothfairy, very little. You'll be bombarded with bumf from people who view a first baby as a major marketing opportunity, but you don't need much at all for months! Your newborn needs to eat, sleep, wear clothes and be transported around - that's it. When in doubt, don't buy - there's virtually nothing you can't buy after the baby arrives, and some things you are definitely better off waiting for.
For instance, different babies and parents suit different slings, so I would always try some at a local sling library after the baby arrives, rather than buying when pregnant. Don't bother with a changing bag at all - after the very first few outings they seem bulky and unnecessary and nearly everyone I know just stuck things in a big handbag.
We bathed DS in a plastic bowl when he was brand new, then he graduated to the big bath with his dad (and still does at 3). Metanium nappy rash cream is very useful if needed. A friend gave us a soft hooded towel, which was lovely, but we usually just used our own old, soft bath towels. No products in the water. Easier to trim newborn nails with your teeth. A semi-circular BF pillow was useful for feeds and for supporting DS once he started to sit up.
You'll be given loads of clothes, so just buy a few basic babygros, a blanket or two, sheets for whatever cot/Moses basket you are using, cheap muslins. A bag of nappies, but again, some newborns are whoppers, some tiny, and you'll be able to gauge better once the baby is here.
The only frantic purchase we had to make in the first few days was bottles, formula and a steriliser when it emerged I couldn't BF.