There are several organisations operating volunteer projects. These are often in remote communities, so this sort of work is not for those who will faint at the sight of a spider.
Activities range from teaching and medical assistance to advisory roles with local area councils. Most are either associated with the churches or with international volunteer organisations.
Most of the following organisations have projects in PNG:
Australian Business Volunteers (www.abv.org.au)
Australian Volunteers International (AVA; www.australianvolunteers.com)
Canadian University Service Overseas (CUSO; www.cusointernational.org)
Japan International Co-Operation Agency (JICA; www.jica.go.jp/png)
Voluntary Service Overseas (British VSO; www.vso.org.uk)
Volunteer Service Abroad (NZ VSA; www.vsa.org.nz)
Two other useful websites that have details for those interested in volunteering:
Global Volunteers (www.globalvolunteers.org)
Volunteer Abroad (www.volunteerabroad.com)