Air Magic:I consider this skill as a must-have. Many Air Magics are among the best spells in the entire game, so making them cost less spellpoints to cast and increasing their effect is really great for a spellcasting hero. In medium to large maps, this skill is almost required to be able to win.
Archery:Archery is useful from the moment that there are 2 groups of relatively strong ranged attackers in a hero's army. (not Halflings and Gogs for example) But I am careful with taking Archery because ranged attackers are hot targets and die fast, so you could end up with a hero with Archery but no ranged attackers left.
Armorer:Armorer is, like Archery, useful in certain situations. Although the effect is hardly noticable sometimes, it does help a lot. It cannot cover the problem of a very low Defense skill, but for heroes with high or medium Defense skills it reduces combat damage more than anything else in the game.
Artillery:Artillery is really ony useful for garrison heroes. It allows them to control the arrow towers during a siege. The damage dealt by the ballista is too low to ever be of any significance. (but a garisson hero without Artillery is often a bad garisson hero)
Ballistics:Ballistics is a lower quality skill that can help a supporting hero to attack towns with an army containing limited amounts of flying creatures/ranged attackers. As the walls go down faster, the foot-soldiers can easily get in the castle. (very useful for Fortress and Stronghold armies)
Diplomacy:The fact that the cost of surrendering drops is not so much the reason why Diplomacy is super, but the increased chance that creatures will join the hero's army is. If you can take Diplomacy, do it! Keep in mind that creatures will be more likely to join if you have some gold in your treasury and if the hero's army already contains that type of creatures.
Eagle Eye:Eagle Eye is bad, extremely bad. I think it is better to conquer the town (and thus learn all spells there) than to learn a spell from a hero from that town. To a garrison hero it may have some use since that hero can then learn spells from the enemy heroes attacking your town.
Earth Magic:Even more than Air Magic, Earth Magic is a must-have skill. Earth Magics are less offensive than Air Magics, but that doesn't make them less good. Most of the time, I am using magics from this school and you really need this skill to complete a medium or large map.
Estates:Estates is nice for supporting/garrison heroes, but for a hero with combat value it is not worth it.
Fire Magic:In my opinion, lower level spells in the school of Fire Magics are far inferior to lower level spells in the schools of Air and Earth Magic. There are a number of powerful higher level spells in this school, but learning Fire Magic doesn't improve their effect as much as the Air and Earth Magic secondary skills do in their schools.
First Aid:This skill is really worth something for garrison heroes. (especially if first aid tents are available nearby) It is much less interesting for fighting heroes, though it can be of some use during long battles.
Intelligence:Intelligence is a great skill for higher level spellcasters. It simply doubles the total amount of available spellpoints, this means that the hero can explore for a longer period of time without having to replenish his/her spellpoints.
Leadership:Leadership is a major skill. It is indispensable in mixed armies and a high Morale gives the hero's troops a serious advantage during battle. (see combat section) In fact, the only situation where a hero couldn't use Leadership is when that hero would be a Necromancer or a Death Knight.
Learning:Learning is nice in the early game because it speeds up the first level ups. In small maps this is a true advantage, but with all other map sizes, it is more of a disadvantage for a main striking hero. (because it is a secondary skill that doesn't really do anything) The effect slowly becomes weaker between hero levels 10 and 20, so take Learning in small maps or for supporting heroes.
Logistics:The further a hero can travel, the better. Logistics is a great skill that you should always take. The more heroes with logistics you have, the faster you will explore and the faster you will grow strong.
Luck:Luck is a nice skill, but not as good as Leadership. The fact that creatures sometimes deal double damage in combat is fun, but a second action in combat is a lot better. I only take Luck for supporting/garrison heroes or if offered a really bad skill as second choice.
Mysticism:Perhaps a tiny bit better than Eagle Eye, this is one of the worst skills there are. In small maps and in the early game the faster replenishing can be of some help, unfortunately in most cases this skill is too weak to be really useful. (10 points/day would be nice)
Navigation:Though the effect of Navigation is even bigger than that of Logistics, this skill is only helpful in maps with truly large bodies of water or for supporting heroes or pirates. The reason is quite obvious: no important events take place on oceans, except for battles. There are no towns, mines, ...
Necromancy:This skill is rubbish if you don't have an undead army. For Necromancers and Death Knights however, this skill replaces Leadership with flying colors. This skill allows its users to build up incredibly huge Skeleton armies that can make a hero invincible. Legions of Skeletons are no exception in Large maps using Necromancy.
Offense:Like Armorer, Offense is useful in certain situations. For heroes with high or medium Attack skills it boosts combat damage a lot.
Pathfinding:Pathfinding is absolutely necessary in maps with lots of rough terrain. In maps without or with just a little bit of rough terrain it is completely useless. I start using Pathfinding when there are more than 3-4 screens of rough terrain, but it starts being useful from 2 screens off I guess.
Resistance:Like Mysticism, I think Resistance could be a relatively powerful skill if the effect was bigger. 20% chance at expert level is much too low (1 out of 5 turns). This skill is better than Mysticism though. For a hero with lots of creatures that have magical resistance already, this skill increases their effectiveness and could be quite useful indeed. (Rampart heroes for example)
Scholar:Scolar is extremely bad, not much better than Eagle Eye, if even better. Could be useful for supporting heroes that start teaching spells to each other, but for any hero with combat value, it is really worthless.
Scouting:Scouting is positively the very worst skill you can imagine. Its only possible purpose could be a safer exploration of unknown territory. (you see somewhat further, so you can see danger coming your way a little bit earlier) But even for secondary heroes this is a useless skill, so never take it.
Sorcery:Like Armorer and Offense, Sorcery is all right in certain situations. For heroes with a high Spell power, it increases damage done by the hero's spells. Sorcery is less good than Armorer and Offense because the effect is only half as big and a hero can cast but one spell per turn, and a lot more combat damage is dealt/received each turn.
Tactics:Tactics is great. Though its effect is limited to combat only, the advantage a hero with Tactics has is incredible. For one thing, you can arrange your troops before combat, hereby avoiding obstruction by obstacles. It allows you to position your creatures in the best tactical formation possible for the upcoming battle. You can also move your creatures forward on the battlefield. This is great for all kinds of armies, (fast or slow) to speed things up and overrun the enemy creatures with all yours on the first turn.
Water Magic:The school of Water Magics is rather weak, except for a few powerful spells. Like the Fire Magic skill, I would only take this skill if the other skill to choose from is worse or if you have access to powerful spells from the school of Water Magics. The spells from this school benefit more from the Water Magic skill than the spells from the Fire Magic school do from the Fire Magic skill.
Wisdom:What can I say, only in a small map (without sub-level) a hero could perhaps do without Wisdom. Not having Wisdom in larger maps decreases your chance of winning more than anything else. A hero with any combat value should have Wisdom, it is the best skill a hero can learn.