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Undead
Only the Necromancer's spell is truly useful, while the others are generally not worth it. Well, if you're playing as a Dread Lord, using Summoning or in a network game with a Necromancer, then Banshee's Wail is decent, but otherwise, I don't take it at all. Eternal Slavery is generally useless; I only take it if there's nothing else to choose from, as Necromancers don't really lose troops anyway.
Humans
Vigil is useful at the start, but less so later on. Prayer is mediocre; I don't take it very often. Experienced Commander is definitely needed if you're playing a retraining build.
High Elves
In my opinion, the most useless abilities in most cases. They're essentially pointless unless you're playing a Chaos build or, less often for an Elf, a Summoning or Darkness build. But I usually play them with a Light build, and in that case, I don't take them at all, unless there's no other choice or they're needed as filler perks. With other schools, Enchanted Arrow and Arrow Storm are needed; Deadly Shot is always the least useful, although you can take it in addition to the other two.
Demons
All abilities are useful at the beginning of the game. The Cursed Sign is especially strong early on. Hellfire is also useful, as is Soul Eater in addition to it. But over time, the usefulness of these abilities decreases. Although Hellfire is tied to spellcasting, the damage bonus is still weaker as the army grows. Soul Eater can be useful at any point in the game, especially against Undead and Mages, to prevent them from regenerating.
Dark Elves
Arcane Wave is a very useful ability when playing a Chaos build, which is usually the case for this faction. Elemental Sense is useful with any build. However, Dark Ritual is the least useful ability, as you're unlikely to want to spend a turn on it. There are times when mana is so scarce that it becomes necessary, but this is rare.
Mages
Mages have powerful abilities. The Wizard's Sign is amazing with many schools; it hardly needs any explanation. Magic Mirror also makes life difficult for enemy spellcasters. Artifact Absorption is useful for the later game, when the army has mini-artifacts, but it's still a powerful ability.
Gnomes
Completed Rune is very useful at the beginning of the game, when resources are scarce and runes need to be used, but it loses its relevance later on. Greatest Rune is, of course, the most useful ability. Completed Rune is already less useful. Often, there's something to cast rather than spend a turn refreshing a random rune. However, it can be useful to keep a permanent Resurrection Rune in the stack in the late game.
Orcs
Reinforcements are useful at the start, but less so later on, although they're always good for Krag. Remembrance of Our Blood is also needed, as Rage is always useful at the start. Resistance to Magic is a rarely useful ability. It requires a lot of spellpower through upgrades or artifacts, and even then, it only works against factions with low spellpower.
Overall, in terms of usefulness, it's something like this:
Mage (all are very useful, although one is only useful in the late game)
Demon Lord (all are good abilities, but some are more useful at the beginning of the game)
Necromancer (one is always very useful, one is almost always useful, and one is not very useful)
Rune Priest (two are quite useful abilities, but one is more useful at the beginning, and one is not very useful)
Barbarian (two are useful, but one is again more useful at the beginning, and one is almost useless)
Knight (one is useful at the beginning, one is useful in a long game, and one is not very useful)
Necromancer (one is very useful, one is rarely useful, and one is practically useless)
Ranger (very situational abilities that are useless when playing a combat build, but are needed when playing a mage, and even then, you don't need to take them all)