Luggage and bags:
Something light, so you can take lots of carvings and baskets back home.
Clothing/Shoes/Weather Gear: Women - make sure you wear modest shorts or trousers only in Honiara, and skirts that cover the knees everywhere else.
Toiletries and Medical Supplies: Mozzie repellant and sunscreen are a must. Don't forget malaria prophylaxis - I usually use doxycycline - it kills lots of other bugs too. Carry paracetamoll - they can be expensive or unobtainable.
Photo Equipment: Extra batteries for digital cameras - they are hard to get at times, even in Honiara.
Camping/Beach/Outdoor Gear: A light spray jacket might be useful. there are no camping areas - you will usually be asked to stay in village houses or rest houses. if travelling by ship, a dense sleeping mat can be useful.
Miscellaneous: I always pack 2 or 3 towels, and also cheap plastic buckets. They are good for doing your washing in, and expensive in Honiara. Leave them behind with the friends you'll make.