Since you asked for it, the possible damage types are:
Smashing
Lethal
Fire
Cold
Energy
Negative Energy
Psionic
Notes:
Technically there is an eighth damage type in the game, falling damage (no resistance to it available, but can't kill you), but I doubt it matters for the purposes of this guide.
There is no electrical damage type, it is energy. The Devs have mentioned this might change, but I'm not holding my breath.
What they have promised WILL change is there will be a Poison/Corrossive type (Poison for say Spines (lethal currently), Corrosive for say Vhazilok spit (fire currently)). What it will be called and what will change to it and what defenses will resist it yet to be announced, or likely even determined.