Alright, so this isn't exactly a campaign but there are individual quests that can be grouped under the umbrella of "Daedric Weapon Quests". These are some of the best weapons you can get in the game with the coolest looks and unique enchantments. There is at least one for each type of player (Warrior, Thief, Mage). I'll go through all the ones I know about so far and add to this post as I finish up a few. There is one weapon/item per daedric lord.
Mehrunes Dagon: Mehrune's Razor - Dagger
This is a fantastic dagger that looks pretty damn cool as well. It boasts one of the highest attack powers in the game second only to the daedric dagger (smithed) and the blade of woe (DB Quest reward). The only reason it doesn't have as much attack power as the aforementioned daggers is that it cannot be upgraded to "legendary" rank via smithing. So its got pretty good attack power, looks cool, but what else can it do? It has a small chance to instantly kill anything you hit. Yep. That includes "bosses" and of course, dragons. It is quite hilarious to walk up to a dragon and poke it once with a dagger and just have it flop down. This enchantment makes Mehrune's razor a valuable asset for an Thief players.
How do I get this?
Remember the letter you get early in the game? The one asking you to come check out the new museum in Dawnstar? Don't ignore this like I did on my first character. Once you get there and talk to the curator running this Mythic Dawn museum he asks you to find pieces of the dagger scattered in various parts of Skyrim. Once you find all the pieces you and the curator head to the Mehrunes Dagon shrine and call on him to assemble it. He has you murder the curator in exchange for restoring the dagger. After you kill him you get the dagger do as you will BUT WAIT! Mehrunes is an asshole and summons two dremora to assault you. After dispatching them you're free to enter his temple and kill two more dremora and loot nice things out of a few chests.
Important note about this quest: Daedra hearts a rarity in this game and are used to craft some of the best (and coolest) weapons and armor so if you're intending to smith stuff this is a good chance to pick up four daedra hearts.
Meridia: Dawnbreaker - Sword
Dawnbreaker is a sword made for killing the undead. It has good base stats and is a good sword for anyone going dual swords or sword n board. When I say it's good at killing undead I mean that with a decently high chance upon killing an undead it causes an explosion that damages and causes all undead to flee. So, if you'd like a zombie exploding sword that I can only assume is made from beating the sun to death and forging a sword from its molten remains, then this is your sword.
How do I get my zombie exploding sword?
If you head to the temple of Marra (location coming soon) you're greeted by a disembodied voice in your head telling you that you need to go and find Marra's beacon that has been stolen and defiled by a necromancer. So you go kill some baddies in a dungeon to find this jewel or "beacon" and Marra asks you to guide her light through her defiled temple in order to restore her power and retrieve dawnbreaker. Once you complete the simple puzzles you're rewarded with the dawnbreaker, a nice addition to any armory, even for mages since you could burn draugr down with spells and switch to the dawnbreaker for the final blow to cause an explosion for any others.
Azura: Azura's Star: Soulgem
This is probably one of the more useful items in the game since you'll probably have several weapons that need to be recharged quite often (especially if you have the blade of woe, ugh its like they used the worst soulgem on that thing x.x) but essentially you go to the shrine of Azura (Just south of Winterhold on a mountain near the dragon's sanctuary thing/word wall) and a priestess of Azura confronts you saying you were fated to come here and return Azura's star to him/her (It's referred to as a prince but appears to be a female figure). The star itself is a soul gem that doesn't break after you use it, which means you can store a soul in it, use said soul to enchant/recharge something and then still have the gem afterwards. In order to do this quest you're forced to find the necromancer who stole it in order to put his own soul into it and ultimately transfer himself to a new host and gain immortality. After you defeat his underlings and retrieve the star you take it to his friend and he puts your soul in there in order to destroy his old colleague. This is also a good opportunity to kill several dremora and gain daedra hearts (This quest + Mehrunes' Razor quest = enough hearts for a full set of armor and a weapon or two). The fight itself is not very hard, just a few dremora and a powerful-ish mage. After the fight ends you're presented with a choice, return the star to azura and receive the purified star which only holds natural souls (nonhuman) or allow the mage to finish his dead buddy's work and turn the star into a vessel for human souls (like a black soul gem). I personally went with the dark star since it can only contain grand souls and I wouldn't yell a bunny to death and have it fill the star with a petty soul.
Namira: Namira's Ring - Ring
When you arrive in Markarth and head into the Jarl's palace you see a conversation between a nord and priest involving an intruder of sorts violating the hall of the dead. After a little persuasion the priest lets you handle it. Upon entering the crypt you meet a woman who claims you're a closet cannibal and verbally abuses you into helping her clear out Namira's shrine of all draugr (apparently they aren't yummy enough for cannibals to eat). So after doing this you're asked to bring the priest to the shrine of Namira. If you choose to continue this quest, be warned, its pretty disturbing. After leading the priest to the shrine you murder him and eat him, Namira rewards you with her ring (+50 stamina and the ability to gain boosted regenerative properties by feeding on your enemies). I found this quest to be quite jarring and subsequently murdered the congregation of cannibals which had no repurcussions other than making me feel better.
Molag Bal (Baal? Bol?) : Molag Bal's Mace - Mace
This is one of the easier daedric weapons to find/get just because the quest literally jumps right in your face if you walk a few steps into Markarth. The mace itself isn't a half bad weapon for anyone using a warrior setup, it has one or two good enchantments (I'll post the stats once I'm back home) and has pretty good base stats.
How do I get mine?
Well like I mentioned in the previous paragraph, if you walk into Markarth just past the inn you'll see a priest standing outside one of the houses who stops and asks you questions regarding the house. He then asks you if you'll come investigate the house with him which begins the house of horrors quest. Once inside you make your way into the basement and then your priestly buddy determines that it isn't a regular daedra like he thought it was and makes a run for the door. The front door is of course, locked, and you hear a voice inside your head telling you to murder the priest. Listen to the voice or don't, the end result is the same. After a few seconds of waiting the priest says "No, no! I don't want to die here!" and attacks you. After killing him the voice invites you down into the basement and into the shrine of Molag Bal where you see a mace and a pool of blood. Then he traps you in a cage and forces you to go find a priest of Boethia for him to torture. Upon rescuing the priest you goad him into coming back to the shrine with you where Molag Bal traps him in the same cage you were in and instructs you to beat him to death or until he submits. After a couple good thwacks with the mace the priest dies and is subsequently resurrected for you to beat to death all over again. Once the priest finally submits you kill him for good and receive Molag Bal's mace as payment. Enjoy your new sadistic toy.
Mask (Can't remember the lord's name)
This item is a heavy class helmet that gives you better prices on things and looks a bit strange. It's got a decent armor rating but the dragon priest masks are better for the most part but it's a funny quest so I'd recommend doing it for a good laugh.
How do I get my weirdo mask?
Upon entering Falkreath (not that you would ever go there for anything but a quest) you're approached by a guard asking if you saw a dog on the road. After telling the guard you were too busy yelling at bunnies and foxes to notice any dogs he directs you to the town's blacksmith who is the one actually looking for the dog. The blacksmith informs you that he just wants a good companion and thought that this stray dog would be a good pet. He gives you a steak to go put on the road in order to lure the dog out but as soon as you head to the quest marker the dog approaches you on it's own. So, this dog starts talking to you in a very goofy voice asking you to come kill some dudes in order to get back to his master. After following the invincible daedric dog for a long damn time (I watched him fight a snow troll, a bear, and some bandits.) you go into a cave and kill all the vampires that inhabit the shrine. Once you talk to the daedric lord you realize that he's kinda pissed that you brought back the dog that he exiled (for reasons that become apparent after traveling with the little bastard) and he has you go retrieve a mystical axe (it kinda sucks) and once you return from fetching the axe you're asked to kill the dog. A tempting offer, sure, but I chose to let the daedric lord deal with him and he gives you the mask as payment for your services and then disappears to go bother people now that he has his full power back (The dog is the source of his power). Yay masks!
I believe that this is all but two of the daedric quests, the other ones that may be considered daedric items are the nightingale armor/weapons which you can refer to my thieves guild post to find out about.
I'll update this after I get home! Thanks for reading!