Man, Clerics get a lot of subclasses. In fact, with 14 published subclasses, they have the most (Wizards are a close second with 13, whereas other classes generally have 7-9). Which is to say we're only going to get through the second half of the Core Books subclasses in this post, with SCAG and Xanathar's making the third post, and Tasha's finishing us off.
Once again, I'm going to be short-handing the level 8 Potent Spellcasting or Divine Strikes feature, as these are common across the whole class, with only Divine Strikes changing its damage type depending on the subclass. The Blessed Strikes feature, an alternative option found in Tasha's, is more versatile but generally does less damage, as it affects both cantrips and weapon attacks, but only ever deals 1d8 damage (which is radiant, so pretty generally useful. Honestly, this might actually not be all that bad.)
But let's get started:
Nature Domain:
Clerics of Nature are worshippers of gods of the natural world. While Life clerics can fit in with any sort of life, this subclass implies a somewhat more druidic aesthetic and appreciation for forests and other natural places away from big population centers (though it would also be a totally appropriate subclass for the Selesnya Conclave in Ravnica, or really any of the other "green" guilds, i.e. Gruul, Golgari, or Simic.
Your domain spells are Animal Friendship, Speak with Animals, Barkskin, Spike Growth, Plant Growth, Wind Wall, Dominate Beast, Grasping Vine, Insect Plague, and Tree Stride.
You also get heavy armor proficiency.
At 1st level, you get Acolyte of Nature, learning one druid cantrip of your choice and gaining proficiency in your choice of Animal Handling, Nature, or Survival.
I don't know that any of these bonuses are really awe-inspiring, though getting an extra skill proficiency is nice. Also, Shillelagh could be a useful option if you want to be a bit more of a combat cleric.
At 2, you get Channel Divinity: Charm Animals and Plants. As an action using your Channel Divinity, you can force every beast or plant creature within 30 feet that you can see to make a Wisdom save or become charmed by you for 1 minute or until it takes damage. While charmed, you can designate it to become friendly to not just you but also other creatures you designate (something I need to remind myself about other charm effects are if the creature has to stop attacking your friends just because they suddenly like you - technically no! Though you'll be in a better position to argue that they should stop attacking your friends.) As such, this can really put a fight on pause... if it's against plants and/or beasts. Could be clutch, but very situational.
At 6th level, you get Dampen Elements. If a creature within 30 feet of you takes acid, cold, fire, lightning, or thunder damage, you can use a reaction to give the creature resistance to that instance of that damage. Now we're talking. While not mind-blowing, the utility of this feature is pretty obvious and strong. Your fighter fail their dex save against the dragon's breath? Halve the damage.
At 8, you get Divine Strike, and you get to choose between cold, fire, or lightning damage. This is actually pretty cool, as you can adjust it when needed based on what you're fighting (for example, against a Flesh Golem, use fire instead of lightning!)
Finally, at 17, you get Master of Nature. When creatures are charmed by your Charm Animals and Plants feature, you can take a bonus action on your turn to verbally command what each of those creatures will do on its turn. While this turns the charm into a much more powerful effect, you're still dealing with two creature types that don't get very high CR monsters. Granted, even at 17 having a bunch of mammoths or treants at your command will still be very useful, but it's situational.
Nothing here is really terrible, but mechanically it's also not terrible impressive. Let's move on.
Tempest Domain:
Arguably another aspect of nature, Tempest domain relates specifically to the many storm gods. I think most people think storms and storm gods are super cool, so let's see how they do.
Your domain spells are Fog Cloud, Thunderwave, Gust of Wind, Shatter, Call Lightning, Sleet Storm, Control Water, Ice Storm, Destructive Wave, and Insect Plague. Obviously a strong theme here (insect plague, though? Storm Sphere is from Xanathar's, right? Because it seems like it'd otherwise be an obvious one.) I also feel like I might have preferred Lightning Bolt over Call Lightning, though over 3 rounds Call Lightning overtakes Lightning Bolt in damage potential - if your fight lasts that long.)
You also get proficiency in heavy armor as well as martial weapons.
At 1st level, you get Wrath of the Storm. When a creature within 5 feet of you hits you with an attack, you can use a reaction to force the creature to make a Dexterity save, taking 2d8 lightning or thunder damage (your choice) on a failure, or half as much on a success. You can use this a number of times equal to your Wisdom modifier per long rest.
Between the armor and the martial weapons, it seems a Tempest Cleric is meant to be on the front lines, and this punishes those who go after you (and being able to choose the damage is great - generally you probably want to go with thunder, as far fewer things are immune or resistant to it.)
At 2nd level, you get Channel Divinity: Destructive Wrath. When you roll lightning or thunder damage, you can use your Channel Divinity to deal maximum damage instead of rolling. This kind of maximizing damage can really increase the damage of a spell - for instance, if you cast Destructive Wave, the thunder half of that (5d6) would normally average out to 17.5 damage, but you can guaranteed it'll be 30. Other than Glyph of Warding, the domain spells actually seem to be the only cleric spells that do these damage types - but that means this could be a fantastic two-level dip for a Storm Sorcerer to get a max-damage Chain Lightning (80 damage to each thing it hits!) or the like.
At level 6, you get Thunderbolt Strike. When you deal lightning damage to a Large or smaller creature, you can push it up to 10 feet away from you. While it'd be great to get this on thunder damage as well, the fact that this only cares about damaging them is pretty great - especially given effects that deal half damage on a successful saving throw should still trigger this. Forced movement without a save is one of the insanely powerful things about Repelling Blast for Warlocks, and being able to just no-save this using, say, Call Lightning is actually really, really good.
At level 8, you get Divine Strike, dealing thunder damage. Weird that you can't choose between thunder and lightning (lightning would be very synergistic with Thunderbolt Strike, but maybe that's the reason.)
At 17, you get Stormborn. You have a flying speed equal to your walking speed whenever you are not underground or indoors. So... not great for an Underdark campaign, but I'm always a fan of features that just plain let you fly (the limitations here are a little annoying, though.)
So, overall, I think that the Tempest subclass is actually pretty good for a more damage-focused cleric. I've briefly played on in Adventurer's League, though only through maybe one or two modules, so I can't really comment too much on them beyond the theoretical.
Trickery Domain:
If you want to dupe your foes with clever maneuvers and be very chaotic, this is a great domain for you. If you have the patience for the four-hour episodes, of which there are over a hundred, I highly recommend you check out Laura Bailey's tiefling trickster cleric Jester Lavorre from Critical Role's second campaign, who is a total delight and a great example of this subclass. Interestingly, I think the subclass actually incorporates some of the abilities that Loki from the Marvel comics and movies uses, which is appropriate given that he's a god of mischief (and thus would be of this domain.)
Your domain spells are Charm Person, Disguise Self, Mirror Image, Pass without Trace, Blink, Dispel Magic, Dimension Door, Polymorph, Dominate Person, and Modify Memory. There are some very strong spells here, giving you both a lot of flexibility in manipulating NPCs and also getting around places safely. (Blink is an underrated survival spell, for example.)
At 1st level, you get Blessing of the Trickster. You can use an action to grant a creature other than yourself advantage on Dexterity (Stealth) checks. The blessing lasts an hour or until you use the feature again (which you can do as many times as you like.) This is pretty great if you want to make it easier for the group to sneak around while the paladin or fighter is clanking around in heavy plate, or just to give the Rogue an easier time scouting up ahead.
At 2nd level, you get Channel Divinity: Invoke Duplicity. As an action, you create a perfect illusion of yourself that lasts for 1 minute or until you lose concentration. The illusion appears in an unoccupied space within 30 feet of you that you can see, and you can move it up to 30 feet as a bonus action to a space you can see, as long as it's within 120 feet of you. While it's up, you can cast spells as though you were in the illusion's space. Also, if it's within 5 feet of a creature that can see it, you have advantage on attack rolls against the creature, as it distracts them.
This is a very good ability, though taking up your concentration checks its power a little. Still, being able to send an incorporeal illusion that can't be destroyed in to tap people for Cure Wounds (or Revivify!) is really great. Also, it'll make it easier for you to land attacks on your foes, which is nice.
At 6th level, you get Channel Divinity: Cloak of Shadows. As an action, you can become invisible until the end of your next turn. You become visible early if you attack or cast a spell. This is potentially a really useful way to get away from enemies, though most of the time you can just disengage instead. Probably best to use Channel Divinity on Invoke Duplicity.
At level 8, you get Divine Strike, dealing poison damage. Given that you don't get martial weapons or heavy armor, I don't know if you'll make tons of use of this, and poison damage is also by a hugely wide margin the damage type most enemies are resistant or immune to. It is thematic, though. But I'd actually seriously consider Blessed Strikes here instead.
Finally, at 17, you get Improved Duplicity. When you Invoke Duplicity, you create 4, not 1 duplicate, and can move any of them up to 30 feet as a bonus action as long as they stay within 120 feet. This is, frankly, nuts. I'd assumed it would be like two duplicates instead of one. But four? You can practically be in 5 places at once with this, so if you need to focus on healing, you can just have each cling to a party member, and if you want damage, you can have them shadow your foes. Nuts, I say.
So yeah, the Trickster Domain has a lot going for it. You can play this as both a strong damage-focused Cleric but also as a very mobile (or effectively mobile) healer.
War Domain:
Finally, we come to the War domain. This is a subclass that can represent the very most vile and evil deities, but also chivalric, heroic ones. It's also one that has its opposite in the form of Peace domain, which we've got like two posts to get through before we tackle.
Your domain spells are Divine Favor, Shield of Faith, Magic Weapon, Spiritual Weapon, Crusader's Mantle, Spirit Guardians, Freedom of Movement, Stoneskin, Flame Strike, and Hold Monster. There's a clear overlap with the Paladin for these spells, which makes sense given that this is subclass has a lot of thematic overlap with the Paladin.
You also get proficiency in martial weapons and heavy armor (which is very on-theme.)
At 1st level you get War Priest. When you take the attack action, you can make one weapon attack as a bonus action. You can do this a number of times equal to your Wisdom modifier per long rest. Given the limits on Divine Strike and how this will likely only be 5 times per day at max, this isn't a ton, but still, more attacks mean more damage, and sometimes you just need that last hit to finish the foe off.
At 2nd level, you get Channel Divinity: Guided Strike. When you make an attack roll, you can use your Channel Divinity to at a +10 bonus to the roll after you see what you've rolled (but before the DM tells you if it hits.) So yeah, again, if you really, really need to make sure that you hit, you can nearly guarantee it. Pretty good.
At 6th level, you get Channel Divinity: War God's Blessing. If a creature within 30 feet of you makes an attack roll, you can use your reaction to grant them a +10 bonus to the roll, following the same rules for Guided Strike. Really, this is just expanding Guided Strike to your allies at the cost of a reaction. Better, more versatile. Certainly not bad.
At 8, you get Divine Strikes, though interestingly, the extra damage is the same as that of the weapon. As such, you'll really want to get a magic weapon to make use of this, but once you do, very few things will resist you.
Finally, at 17, you get Avatar of Battle. You gain resistance to bludgeoning, piercing, and slashing damage from nonmagical weapons. The nonmagical restriction hurts a little at this level, though at the same time, a ton of monster don't, actually, have nonmagical weapon attacks, including the Tarrasque and almost all dragons.
Phew - we've finally gotten through the PHB Cleric subclasses. With those done, we only have six more to go - one from SCAG, two from Xanthar's, and three from Tasha's (one of which was a reprint from Guildmaster's Guide to Ravnica.)
Overall, I think of the PHB ones and the Death Domain from the DMG, Life domain is the clear winner if you just want to focus on healing. For damage output, I like Death and Tempest. And Trickery is actually very versatile. We'll see as we go beyond the core books if we get some more unique and interesting features, though there are plenty of choices here that are totally worth trying.