
Azothath |
invisibility:I2
short description; Invisibility{Y}: Subject is invisible for 1 min./level or until it attacks.
from the spell description; For purposes of this spell, an attack includes any spell targeting a foe or whose area or effect includes a foe. Exactly who is a foe depends on the invisible character's perceptions. then spells that only effect allies is given a pass.
the key work is "attack" in the short description. It doesn't have to be damage and many GMs would agree that forcing a target who is a foe to make a save would end invisibility even if it is harmless. Then "whose AoE includes a foe" is another "no" zone.
So you need indirect spells like; summon monster, create pit in an area free of foes at the time of casting, etc.
The normal casting of Euphoric Cloud ends the caster's invisibility as its AoE contains foes at the time of casting AND it forces targets in the AoE to make saves. Now if cast in an empty hallway that foes have to traverse later... the caster maintains his invisibility spell.

Mysterious Stranger |

While Euphoric Cloud does not deal HP damage it does give the target a harmful condition. Not being able to take actions and a penalty to skill checks is harmful. So, yes this would break the spell invisibility.
One thing I would bring up is that the rule on attacking breaking invisibility is on the spell itself, not the ability invisibility. If the ability that is granting the ability to become invisibility does not reference the spell, attacking does not break invisibility. Most abilities that allow you to become invisible do reference the spell, but not all do.

Pizza Lord |
Like Azothath stated, casting the spell euphoric cloud will not break the invisibility unless you include an enemy in the area of effect. If there's even one, even an invisible one you couldn't see or weren't aware of (but would consider an enemy), then your invisibility would break.
Otherwise you can cast it in a free space and if they entered it later you wouldn't have to worry. It's the same deal with something like wall of fire. If cast the spell and it intersects an enemy or is even close enough to deal heat damage when it forms (within 20 feet of the heat-emanating side), you will break invisibility. If you put it up and they walk into it later, you are fine. Or you could create a ring around an enemy with the heat-emanating side facing outward and still be fine, leaving them trapped inside and forcing them to cross it on their own.

AwesomenessDog |

Another notable point is that the spell doesn't even have to necessarily affect the foe to pop invisibility, they just have to be in the area. An example would be casting fog cloud with an enemy in the radius of the smoke; the smoke doesn't do anything but obscure vision but by being in the area, it triggers the AoE clause.

Anguish |
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Rule of thumb: if you want to do it to an enemy, it's almost certainly going to break invisibility.
Cast cure light wounds on an ally because they're hurt? No problem.
Cast fly on yourself so you can get away? No problem.
Cast flesh to stone on your target so they're screwed? Not allowed.
Cast black tentacles around your target so they're screwed? Not allowed.
The closest thing to allowed is stuff like casting wall of stone between them and you. Yes, you made it so they have to around it to get to you but you didn't do anything to them.

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The spell ends if the subject attacks any creature. For purposes of this spell, an attack includes any spell targeting a foe or whose area or effect includes a foe. Exactly who is a foe depends on the invisible character's perceptions.
Note that
For purposes of this spell, an attack includes any spell targeting a foe or whose area or effect includes a foe. Exactly who is a foe depends on the invisible character's perceptions.
doesn't limit "an attack" to "who is a foe depends on the invisible character's perceptions", it adds that to the list.
If you try to cast a spell on someone you consider a friend but who considers your act an attack (like a Confused friend) you are attacking him, even if, from your point of view you are helping him.
When checking if something is an attack, you first check if the action is an attack in the general sense of the term, then, if not, if it is an attack in the spell definition.
Offensive actions like Summoning creatures or casting spells in empathy areas aren't attacks.
Last but not least, the caster can't play mental gymnastics trying to say that a foe is a friend. What matters is his real opinion.