In short, Riders are by far the most versatile and superior land unit, at least until the late-game where Knights are used in some multiplayer games. Units unlocked by a tier 3 technology are mostly used late-game in multiplayer games. Knights are typically the strongest of these units, especially given that all of these units have the same technology costs. Other units typically see use starting earlier in the game.
Warriors: Warriors are mostly used for early-game exploration. Once battle begins, the production of Warriors generally ceases in favor of Riders. Any remaining Warriors can be used for front-line defence, as they have a stronger defence than Riders, but be cautious not to let the less-mobile Warriors impede the movement of Riders. (In general, attack with Riders before Warriors, since Riders can be moved after attacking with their Escape ability.)
Defenders (a.k.a. Shields): Defenders are the best for naval units given their high health and low cost. Defenders are also very useful for stopping Knights (remember that enemy units cannot move past your units). Also, Defenders can be used as a stopgap measure to stop invading enemy units (especially early-game), but, in many cases, if you are under attack and are this desperate, you will be better off starting a new game. Sometimes, Defenders are used to explore enemy territory (as opponents typically will not attack Defenders unless they have ranged units). The main weakness of Defenders is that they virtually cannot be used to attack enemy units (barring those that can be killed in one shot). Also, Defenders are not mobile at all and may hinder the movement of your Riders, etc. This leads Defenders to be more annoying to play against than useful to play with when used on land.
Swordsmen: A late-game unit like Knights, Swordsmen (SM) are typically used when many Mines are already used (leading Forges to be effective), making Smithery much more worth it than purchasing both Free Spirit and Chivalry for Knights (especially since those two technologies have practically no other uses). SM may also be used to counter enemy Knights.
Mind Benders: Mind Benders (MBs) are the weakest and least-used unit in the game. They die too easily, especially to mounted and ranged units, and are limited in movement; Meditation and Philosophy do not have many effective uses (a small defence bonus on a limited number of tiles and a discount to technologies that does not matter by the stage of the game MBs are researched), and competent human players will nearly never allow their opponents an opportunity to convert their units. However, MBs can also be used to support friendly troops (they can heal adjacent friendly units by 4 HP).
MBs never see more than limited use, mainly against bots. Against humans, MBs mainly serve as a deterrent and support unit (and can be especially annoying if hidden in the fog to convert an enemy unit, super units in particular), but competent opponents will easily eliminate them by using ranged or mounted units.
An exception to the uselessness of MBs is Polaris, which can convert frozen enemy units (often frozen with an Ice Archer). However, this so-called “Ice Bender” strategy is rarely used in practice, not only due to the limited movement of MBs but also because, for the same technology cost, Knights are more effective (especially when paired with Polarism and/or Roads).
Riders: Riders are the most versatile and useful units, a fact I think is best demonstrated through case studies, such as the first 15 minutes of this video https://www.youtube.com/watch?v=V5VMFGbfXnE by Tupp (which I highly recommend you watch just for the sake of demonstrating early-game economic development and the usefulness of Riders combined with roads, even if you are not interested in Perfection) and this video https://youtu.be/wMwYAl5kdtc by Unwise. In addition to just a higher movement stat, the escape ability (allowing Riders to move after they attack) gives Riders extreme maneuverability. This allows them to travel long distances (striking enemies far away or entering battle after being trained from faraway cities), quickly grab villages and ruins, “bounce” into unoccupied enemy cities, especially very early game when they can jump out of the fog and ambush an enemy city (Never leave your cities open if they are at risk for an enemy Rider attack like this!), and control large swathes of territory (as demonstrated in Unwise’s video). Also, Riders do not get stuck at choke points because of their escape ability. Riders are especially deadly when used with Roads.
Knights: Although their most memorable use is their persist ability, allowing them to eliminate swathes of Catapults and other 10 HP units in a single swipe (but not those with a defence bonus!), Knights are useful simply as a unit with a very high movement stat (especially when combined with Roads) and a strong attack. However, although Knights do have 15 HP, they still have a weak defence. Besides, enemy Defenders (or SM) can greatly hinder Knights. (Those are best dealt with using ranged units and sometimes-sacrificial Riders in addition to Knights.)
Archers: The use of Archers is one of the most controversial topics among the competitive Polytopia community, with some swearing by their utility (especially in the ‘killing not wounding’ strategy or “just hitting things with ‘em”) and others regarding Archery as something they would never spend stars researching. Pairs great with melee units, and perfectly with swordsmen since together they can two-shot 10 HP units and not take any damage.
Boats: The weakest unit in the game, created when a unit moves onto a port (The unit will have no more actions after this apart from upgrading). Has the Hitpoints of the original unit (making defenders the best value for stars). Mainly used for getting to a village or ruins on ocean tiles, but otherwise for increased Mobility (and attack) should be upgraded into a ship.
Ships: Created when a boat is upgraded for 5 stars, increasing movement, attack, and Defence to greater than an Archer. Great for supporting in Land battles but from the sea where the enemy will find it hard to retaliate.When exploring it is much better to travel in pairs so the fog doesn’t limit mobility.
Battleships: Created when a Ship is upgraded for 15 stars (with a net cost of 20) making it the most expensive unit in the game. These are extremely useful in naval battles with strength comparable to a weak Super Unit and can one-shot 10 Hp units. The scout ability works excellently at sea to find ruins, and it is much better to travel in pairs. These are great units all around.
Dragon: The Super unit for the ∑∫ỹriȱŋ tribe. When a city reaches level 5+, it can produce a Dragon egg. After 3 turns of being on the square, the egg will grow into a Baby Dragon. If the Egg was in a boat, the boat would disappear and the Baby dragon would take its place. Baby dragons are essentially flying riders with double vision, they can fly over water and are great for exploration too. After another 3 turns, the Baby dragon will become a Fire dragon. These are ranged, high-damaging splash units that can fly. These are great in the second line of your attack so they are away from any damage, and their Splash attack can prove very useful for destroying clumped-up hordes from a range. Be wary of catapults, as Fire dragons only have 20 HP and will be 2-shot by them.
If a Dragon egg enters a port it will remain a boat until the three turns of growth are up and it will become a Baby dragon replacing the boat
Polytaur: Created when a forest tile with an animal has the ‘Enchant animal’ action used on it.
Navalon: Created when an ocean tile with a whale has the ‘Enchant whale’ action used on it. Navalons are just like knights, but on steroids (and water). They have a lot more HP, lots of mobility across water, a ton of defence, and a bit more attack, allowing them to best 10 HP units even with a defence boost and along with the persist skill can go on some nasty combo runs. To boot, unlike their draconic counterparts, they can enter and capture cities since city tiles are counted as water tiles. The Navalon also has the unique Navigate skill, meaning it can explore ocean tiles even without Navigation unlocked.