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Undead:
Skeletons (the un-upgraded version is quite weak, but the upgraded version offers ranged attacks or a host of other benefits)
Liches (otherwise, they're not very effective without spells)
Humans:
Griffins (their attack and other abilities provide a noticeable advantage)
Monks (again, for the spells)
Knights (speed and other useful bonuses)
Angels (2 speed and bonuses, or spells)
High Elves:
Fairies (initiative and other bonuses)
Bladedancers (noticeably higher initiative, plus attack or defense-enhancing bonuses)
Druids (more spells and very useful bonuses, such as increased spell power)
Demons:
Imps (noticeably better health, and they send stolen mana to your benefit)
Dogs (immediate speed boost, triple attack, and retaliation, which is much better than the un-upgraded version)
Succubi (chain and seduction provide a noticeable advantage)
Cerberi (speed and aura boost, as well as a decent health increase)
Dark Elves:
Scouts (they're useless without poison)
Beasts (retaliation makes them much more useful)
Hydras (noticeable health increase, plus 3 heads, and other benefits)
Dragons (immunity to magic greatly buffs them, but other bonuses are also useful)
Wizards:
Goblins (another upgrade where the advantage is very large compared to the un-upgraded version, at least almost twice the initiative, and various machine-related abilities are useful)
Gargoyles (more health, more magic immunity, or, conversely, an enhancing aura)
Rakshasas (ferocity makes them noticeably more useful)
Colossi (ranged attack already provides a noticeable advantage, plus bonuses)
Dwarves:
Mountain Guards (almost twice as much health, plus various bonuses that increase defense, making them much more durable)
Bear Riders (it's their bonuses that make them stand out, while the un-upgraded version has nothing like that)
Bone Throwers (again, the un-upgraded version is useless, while the upgraded versions have very useful bonuses)
Priests (they are mainly taken for their fire spells)
Orcs:
Goblins (both health and very useful bonuses, and they no longer betray)
Shamans (the ability to replenish mana, plus more spells or other benefits)
Punishers (they are better in damage, or have many very useful bonuses)
Cyclops (they can become ranged attackers, plus a good attack bonus)
There are, of course, many other units whose upgrade is noticeably more useful, but I have highlighted the main ones in my opinion, although this is all situational. There may be situations where upgrading other units is more useful.