"Dungeons towns are built by Warlock and Overlord hero types to act as bases from which to wage campaigns of conquest for wealth and power. Similarly minded creatures are attracted as allies. Other Dungeon creatures are in thrall to their masters. Dungeon armies are possessed of a variety of long range attacks, have effective damage dealing troops, and have the ability to greatly disrupt the strategies of their enemies." RoE manual
Some may find the information in this section subjective or irrelevant.
Upgrade the level 2 creature dwelling as soon as possible: Harpy Hags have a huge speed increase (6->9) and gain no retaliation.
Upgrading Medusas to Medusa Queens is more crucial than Beholders to Evil Eyes, because a Medusa Queen has eight instead of four shots, while a Beholder already has twelve. Getting an Ammo Cart (from Inferno's, Stronghold's or Tower's Blacksmith, or at a War Machine Factory), will help a lot, since Medusa Queen's eight shoots are still not sufficient for a fierce battle.
Bless your Harpies/Harpy Hags (Dungeon has a 19% chance to get Bless). Harpies/Harpy Hags have damage range 1–4. Instead of on average 2.5, with basic (advanced) Water Magic they will consistently do 4 (5) damage, a 60% (100%) increase. Similarly, Curse the enemy's Harpies/Harpy Hags (Slow would also be useful since Harpy Hags have a decent speed).
Haste your Minotaurs/Minotaur Kings. They are brutes which do a lot of damage and you want them to strike at the enemy as soon as possible. In addition a hasted Minotaur King can reach nearly any point of the battlefield given no obstacles.
Beware of Red and Black Dragons' breath attack which can damage your own troops.
Dungeon is expensive to build, has good magical capabilities (e.g. Mana Vortex and level 5 Mage Guild) and powerful troops like black dragons, which are among the strongest creatures in Erathia.
If there is a high level creature dwelling which can be conquered early, it may be beneficial to wait flagging other creature dwellings. This allows to recruit the high level creatures every week from both the Portal of Summoning and the dwelling itself. The Portal of Summoning selects its units every week randomly from all creature dwellings you have flagged. For example, if there are Red Dragons and Troglodytes available on the adventure map, it is beneficial to not flag the Troglodyte dwellings to recruit more Dragons.
Playing against Tower which has Titans who hate Black Dragons, try to use the following tactics so as to avoid Black Dragons' losses (see Cons). If Titans are behind someone else, attack that unit with Black Dragons, and breath attack will do 150% damage against Titans due to Black Dragons' hate against them. It works even if Black Dragons targeted another stack, and Titans won't retaliate.
Two ranged units, both of which have no melee penalty.
Mana Vortex: doubles your max spell points once a week.
Black Dragons are immune to all damage or debuffing spells, and they are candidates for the "Dragogeddon" tactic because of their spell immunity. Armageddon spell is available in Dungeon, unlike Rampart or Conflux which also have units immune to it.
Warlocks gain more Spell Power than other hero classes.
The weekly income with Capitol and the Resource Silo is enough to recruit all the units without any external mines.
On a map with two layers, Dungeon will get a huge advantage as any battle in the underground will be fought on subterranean terrain, thus Dungeon units will get speed bonus.
Cons
Dungeon is quite expensive to build it up.
Manticores are one of the weakest level 6 units, and even when upgraded to Scorpicores they are significantly weaker than Naga Queens or Dread Knights.
Black Dragons are immune to any benevolent spells, including Resurrection.
Difficult to build level 7 creature dwelling.
Basic Pillar of Eyes which is level 3 creature dwelling requires each type of resource, and is necessary to build all higher level creature dwellings, making Dungeon possibly the worst town for playing on Impossible level.
There is no hero with Medusa specialty, unlike other towns which have heroes specializing in 4th level units. It's not a big problem, but Medusas still might want to be buffed, as they are rather slow, often forced into melee due to low amount of shots and lack of Ammo Cart, and generally weaker than Crusaders and Vampire Lords.
If the map has only one layer, Dungeon will get a disadvantage since subterranean terrain is used rarely without underground layer, and in most cases any other faction will get a speed bonus unlike Dungeon.
Overlords cannot learn Water Magic, therefore being unable to cast Bless on the entire army, while many Dungeon units have significant damage range (especially Harpies and Minotaurs).
Beware Titans who hate Black Dragons. Titans and Black Dragons have similar stats, possibly sharing 2nd-3rd place in the whole game after Archangels, but Titans have an opportunity to shoot Black Dragons to death, and if Black Dragons force them to melee (which is possible as Black Dragons are faster), Titans will still do 150% damage by retaliation. Impossibility of Black Dragons' resurrection makes it a big problem.
Prayer is banned, while this spell may help Red Dragons (but not Black) a lot since they're immune to Bless, Bloodlust, and Haste. (Rampart's Green Dragons are susceptible to Prayer as well, and in Rampart this spell is available.)
Castle
Rampart
Tower
Inferno
Necropolis
Dungeon
Stronghold
Fortress
Conflux 
Cove 
Factory 
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Necromancy and 
Water Magic are not available for overlords.
Resistance and 
Interference 
Troglodyte 
Infernal Troglodyte
Harpy 
Harpy Hag 
Beholder 
Evil Eye 
Medusa 
Medusa Queen 
Minotaur 
Minotaur King 
Manticore 
Scorpicore 
Red Dragon 
Black Dragon