*Light Water Reactor (LWR)
- Boiling Water Reactor
Purpose - electricity
Coolant Type - water (H2O)
Moderator Type - water

- Pressurized Water Reactor (PWR)
Purpose - electricity; nuclear powered ships
Coolant Type - water
Moderator Type - water

*Heavy Water Reactor (HWR)
Purpose - electricity; plutonium production
Coolant Type - heavy water (deuterium oxide, D2O)
Moderator Type - heavy water

*Graphite Moderated Reactor
- Gas Cooled
Purpose - electricity; plutonium production
Coolant Type - gas (carbon dioxide or helium)
Moderator Type - graphite

- Water Cooled
Purpose - electricity; plutonium production
Coolant Type - gas (carbon dioxide or helium)
Moderator Type - graphite

- Liquid Metal (LMFBR) (most common type of breeder)
Purpose - electricity; plutonium production
Coolant Type - molten, liquid sodium
Moderator Type - N/A

http://www.ieer.org/reports/npd-tbl.html Source