(serf's parma)
If a mage reduces a ghost's might to below zero, is it effectively destroyed? Or does it reappear once it regains might?
Either of the above or something else, no hard and fast rules.
However, as a SG, I'd recommend that their be some way to destroy it, tho' traditionally that sometimes that involves a clever action to put the spirit to rest rather than a brute spell. 
Ex:
(I believe from the Bros. Grimm, and forgive if my memory is flawed in the details. The story arc is the same.)
There are many ghost stories (esp Japanese!) where the ghost is doomed to repeat a mistake or moment of bad luck for eternity (sometimes involving/inflicting their doom on the living), until someone can break the cycle.
Other examples are the grateful dead stories*, where a living being does a favour for a spirit/skeleton, such as blowing pipe smoke or pouring beer into the skull, or some more complex task, and the troubled spirit is eased so it can "rest in peace".
(* yes, where the band got its name)
If I were to combine these two approaches (Might reduction and curse-removing), I'd have the spell remove the ghost only for a short time period, perhaps until the anniversary of its death or the incident that led to its death, and then it would reappear, same as before.
To quote some of the text from Lay to Rest the Haunting Spirit (ArM5, p.150):
So it appears that the ghost is a goner, but there's maybe enough wriggling room there for an SG to bring one back.
Cool. I just wanted to make sure I wasn't going to get a rule wagged in my face if the characters returned to a vis source to find the ghost there again. This time they might think about how to soothe it's soul, rather than just dispelling it.
Thanks!
eric
Which by the way is path to take if you'd want to lay the gosts of Calebais permanently to rest. And I like the dramatic pull of having to help the ghost to terms with it being dead and untangling whatever it is that keeps it fettered to the mortal realm. But for other stories other kinds of ghosts, that might be 'killed' out right or by some other means (bringing the feather of Icaros to the haunting place at midnight on the summer solstice) could be better. So in many ways it's perfect that the RAW has made no firm ruling on the fate of zero-Might (Score) ghosts.
As a comment to all new SG's, be aware of your "habits", and what your players "expect". If they are used to brute force to overcome all obstacles, then this sort of elegant solution may be an unexpected puzzle to them, and frustrating because of it.
If your players are used to having to "beat up" on anything they meet, then maybe have some "old wise man" figure available, but not obviously connected (ie, bring them in a while before), who could be questioned about uncooperative ghosts. Let them get used to whatever rhythms you want to put into the story before forcing it onto them.
And another thing- don't get glued to only having only one narrow "correct" path to solve the problem! If the players have been creative and RP'd well, and have come up with a "reasonable" solution, consider changing the goal to fit a "close enough" approach - sometimes rewarding creativity (and moving the story forward) is better than slavish fixation on one "right" solution which stalls the story for an entire session.
we had a situation where a version of DOE was only temporary (ghost reformed at sundown) you needed to use a mentem effect to permenently remove the might.
Think of Sauron.
You got to destroy the ring to destroy Sauron. If not, you can beat him but eventually he will come back, so the ring wraith etc.
I always tought it was a good story arc and a good move by Sauron to have put a significant part of his life force in a magical object. IMO, all ghost have a kind of physical or metaphorical link that, if broken, would send them in the afterlife (wathever that is).
-Bellysarius
hehe 
Okay no worries, I'll not charge this as an spoiler.
The problem is that most of your power is in the ring...
Most but not all.
Even after the destruction of the physical link, it's possible for the ghost to wander without even be able to take form (my first example still apply to this case). It's almost the same thing as behing destroyed.
In my saga, the destruction or breaking of the metaphorical link + the reduction of the ghost might at 0 would mean a complete obliteration of the ghost.
-Bellysarius
Related, belated question:
Do Ghosts/Spirits exist that have other than Magical Might?
(At first glance, I feel that Infernal Ghosts/Spirits could exist, tho' they'd be rare, and have to have been really evil to manifest as such.)
What about Fae ghosts? Divine??? (Or would these not be "spirits" in the same sense???)
The reason I ask if for Wards, but also curious as to general consensus.
Also, if a given Spirit could be either Magical or, say, Infernal, could a Ward vs Magical Spirits be augmented to also be a Ward vs both Realms for an additional Magnitude of complexity? All 4 Realms for +3 Magnitudes?
Thoughts?
Yes.
Infernal ghosts are mentioned explicitly in Realms of Power: The Infernal.
I believe these are mentioned as a possibility in The Mysteries and in Calebais.
The Divine mentions "righteous ghosts" in the section on the Jewish tradition. I imagine saints also fill this role in the Christian tradition.
I'd say no. I can't think of any other spells that allow that-- either it affects the form, like a ReHe spell that affects plants, or it affects creatures with a particular type of Might, like a spell that affects Herbam faeries.
Well, in theory, why not?
This is like making a ward against heat and flames also usefull against terram.
Problem is, of course, this doesn't use 2 different forms, but Vim in both cases.
On the other side, the Aegis sort of does this kind of "ward against all", so it has already a kind of predecessor.
Thus, I would probably allow it, although maybe with an added complexity for each additionnal realm.
This is a problem? Seems like an open invitation to me.
Really? How about any spell with another Form requisite, that adds a second effect to the first. Only, as tf points out, this doesn't even require a second form, it's just a different application of the first.
With an improvved ReMe spell, could you not rego both Human Minds and Spirits? With ReIg, can you not move both heat and light?
Interesting choice for an example. ReHe guidelines allow both Warding vs Creatures (general) and Warding vs Mundane Plant Products (Lvl 15) - could those not be combined, if a Mag or three of complexity were added in?
And, as tf mentions, AotH covers all bases, equal opportunity.
Now the counterarguments would be that Aegis is an extremely atypical, non-Hermetic spell, and so on.
For me, the best counter-argument lies in the fact that Rego Vim Guidelines for Wards say "A spell of this nature will only ward against creatures from one Realm", but that begs the question- "what is 'of this nature' ?" That could just as easily refer to defining the baseline of the spell, as defining it vs 1 Realm, not all of them, i.e. "of this nature" refers to a spell that guards vs Creatures < Level, which is the first, defining sentence of that sub-section, and doesn't refer to a spell "against creatures of one Realm". (Ain't English wonderful?)
So, a spell that guards vs Creatures of 2 Realms would be of a different "nature", in that they guard "vs Creatures < (Level-5)", or whatever.
Dunno- as I said, I can see it either way, that's why I'm asking.
Exactly.
Such a spell would be less efficient than an aegis: While an aegis wards against any creature with might of its level, such a spell would ward against at most any creature with might of its (Level - 15), less if adding another modifier for complexity.
Moreso, it wouldn't have the spellcasting penalties of an AotH, making still the Aegis the superior spell an breakthrough it is supposed to be.
On the other side, it would be far more flexible than an AotH, as you could create these Circular Wards against Supernatural Creatures without the need of a ritual (so long as final level is beneath 50).
Anyway, this doesn't seem overly imbalancing, as the same magus could probably cast 4 different circular wards. 4 spells to learn, but they would probably be more efficient.