[忍]

What elemental damage do spirits do? Fire spirit is obviously fire, but what about the others?

[Rosa]

Traditionally
Water = cold
Air = lightning
Earth = acid ( weird  one indeed  )

As of Street Grimoire I guess water can choose between cold and water

It was much more interesting in 4th edition when you had elemental effects like blast, sand, metal, light, smoke and the traditional ones.

[Kiirnodel]

If by "traditional" you mean based on what D&D says elementals are associated with, sure.

In Shadowrun, spirits aren't necessarily forced in the same way. The spirit's form determines the element of the attack, and that is usually determined by the tradition and outlook of the summoner. An Air spirit that manifests as a whirling tornado might deal electrical damage, but one that shows up as a manifestation of the bitter north wind would probably be more appropriate as Cold damage. I could even see a Spirit of Fire having electrical damage instead of fire (for a spirit that is more "energy" than pure flames).

The choice of element should be chosen at the time of summoning, and like optional powers, can't be changed. I also usually restrict my players to a particular style of spirit. That is to say, once they have decided what sort of theme their spirits take, they usually stay that way (the Cat shaman that always summons Beast Spirits that are felines isn't going to suddenly summon a Beast Spirit that looks like a snake). That will sometimes dictate what the element is, (for example, Fire spirits usually have some sort of fire theme, so they are usually fire element) but the spirits with the element as an optional power are more likely to be able to change slightly.

[MijRai]

I've had an Aspected Conjurer who summoned Guardian Spirits, and Guardian Spirits can have Elemental Attack of your choice.  He would summon different element Guardian Spirits depending on the situation, with the idea that those spirits each had a little bit of difference between them, but still all hailed from the same region his Tradition called on.  Fire was the most common, so they could have flaming swords, but once or twice he did cold or electric, with appropriate aesthetic changes.