Maybe look at something like Star Trek Online or Space Empires too. STO has things like Phaser, Disruptor, Anti-Proton Beam, Phased Polaron Beam, Photon Torpedo, Quantum Torpedo, Plasma Torpedo, Chroniton Torpedo, etc. SE has things like incinerator beams, graviton hellbores, meson blasters, etc, and specialized psionic, crystaline, temporal and biological weapons. SE doesn't have damage types like an RPG would, but it has weapons like ionic disruptors which specifically target engine components or phased polaron beams that ignore normal shielding but not phased shielding, or point defense weapons which can damage fighters and seekers but not ships or planets, or anti-proton beams that do more damage at close range and less damage at long range. GURPS also has sci-fi campaign settings you could look at.
I can think of:
Kinetic
Heat
Freeze (or Anti-Heat, Absolute Zero, Exothermic, etc)
Electron/Electrolaser
Acid/Alkaline
Bio-Virus
Cyber-Virus
Waveform/Sonic/Seismic
EMP
Plasma
Photon (In sci-fi, consider also photonic molecules)
Ion
Radiation
Atomic (like an actual atom bomb or something that destabilizes or aggravates nuclear forces)
Inertial (or Anti-Inertial, a weapon or power that modifies the properties of inertia)
Neutron/Neutrino
Entropy Wave
Disintegrator (something that breaks down chemical bonds or atomic structure)
Graviton
Anti-Matter
Dark Matter
Dark Energy
Quantum (whatever sort of sci-fi technobabble you want)
Strangelet
Exoticle (Exotic Particle, similar to a strangelet or strange quark but make up your own rules)
Hyperspace/Wormhole/Warp (something that causes space-time to distort)
Phasic (i.e. makes things out of phase)
In terms of game design, I would try to think about what you are using them for. Like, is it a matter of humans using photon weapons while space-elves prefer plasma weapons and space-dwarves prefer graviton weapons? Would it be something like robots are susceptible to EMP and cyber-virus but not diseases or radiation, or humans are susceptible to psionic attacks while space-elves are not? Do elements cause special status changes, like Heat attacks causing burns or radiation causes cancer? How do you protect yourself from different elements, do you wear a dark-matter proof suit or adjust your shield frequency to compensate for the effect of disintegrators? Would using equipment cause you to become weak to certain elements, for example, if you're using powered armor, would it make you weak to EMP attacks or can a heat beam be disabled if hit with a freeze ray? How does a player sense what will be susceptible to something like inertial or photonic weapons?