A fireball is cast and is about to deal 8d6 damage to five different opponents.
Do you roll 8d6 one time and each of the five opponents takes that damage (subject to saves), or do you roll 8d6 for each opponent, giving each opponent a unique damage amount?
It's a play-by-post game so time saving isn't a factor. We're looking for whatever the rules prescribe.
The spell's description, states that the amount of damage done by the spell is based on the caster's level1: 1d6 per level, up to a maximum of 10d6. Your 8th level caster has sent a fireball to burn their enemies in a given area. I would expect to see in the spell's text something like "roll Xd6 for each creature in the area of effect" if there was a need to roll more than once.
Damage
Damage is determined by rolling the dice listed with the weapon. {snip}
Spells do their listed damage.
Spells specify what they can target, what their effects are, and how they can be resisted or negated.
The cast a spell section in Combat does not call for multiple rolls if there is more than one target affected.
Subjects, Effects, and Areas
If the spell affects creatures directly, the result travels with the subjects for the spell’s duration. If the spell creates an effect, the effect lasts for the duration.
The targets' means of influencing spell damage is by either making a saving throw, or being resistant, or even immune, to the spell's result. That will vary with each target.
Saving Throws
The saving throw entry in a spell description defines which type of saving throw the spell allows and describes how saving throws against the spell work. {snip} Half The spell deals damage, and a successful saving throw halves the damage taken (round down).
Since the spell doesn't call for a separate roll for each creature in the area of effect section, the clearest interpretation of the spell's result is that the damage done by the spell is rolled once: by the caster (or by the GM if you prefer). The caster's fireball will do 8d6 fireball damage as mitigated by each targeted creature's saving throw, resistance, and/or immunity.
I didn't find a place in the SRD that precludes rolling separately for each target, so you could do that. (I don't see the point, but you all do what's fun for your table).
When looking at "the spell's result" and "special effects" there isn't a further general guideline on rolling separately for multiple targets in an area of effect.
Once you know which creatures (or objects or areas) are affected, and whether those creatures have made successful saving throws (if any were allowed), you can apply whatever results a spell entails.
The result is generated by the caster based on their level. Those in the area deal with that result in various ways (or they don't and they receive the full effect).
Special Spell Effects
Many special spell effects are handled according to the school of the spells in question. Certain other special spell features are found across spell schools.Attacks
Some spell descriptions refer to attacking. All offensive combat actions, even those that don’t damage opponents, are considered attacks. Attempts to channel energy count as attacks if it would harm any creatures in the area. All spells that opponents resist with saving throws, that deal damage, or that otherwise harm or hamper subjects are attacks. Spells that summon monsters or other allies are not attacks because the spells themselves don’t harm anyone.
A similar area of effect attack type is described there, but again nothing is mentioned about each target's damage being rolled separately.
Finally, the item deals splash damage (if any) to all creatures in the square it lands in and in all adjacent squares.
... so they decided to spell it out in a recent edition of D&D. In that edition, roll once is the clear rule
1 FWIW, this is how fireball worked in the original game (published in 1974) from which PF grew. Each edition has had a number of changes, so assuming that had not changed would be a step toward error. For example, in the original game there was no cap on how many d6s you could roll; if you got to a high enough level, fireballs did some insanely high damage.
