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When I first saw Zephrys, my mind was blown. Trailing on this was the memory of my mind being blown by other cards in the past, just less so. Blizzard definitely keeps coming up with novel ideas and so I decided to go through the past expansions and see which cards had this kind of effect on me back then, so here's the list. As I often do, I maybe went a little overboard, so if you don't feel like reading all this crap I just typed, scroll to the bottom to get just the names.
Classic
There is only one choice really: Lord Jaraxxus. Ben Brode's favourite card (also 2nd, 3rd, 4th and 5th favourite card), the battlecry of this famous karaoke singer was by far the most interesting effect in the base game and comes with a cool animation to boot. INFERNO!
Honorable mentions go to the Hall of Fame cards (previously "Promo") Gelbin Mekkatorque and Elite Tauren Chieftain, former for the wacky outcomes that have the same odds of helping you or your opponent and the later for a kickass intro that went unchallenged until Goblins vs Gnomes.
Curse of Naxxramas
The tag team of Feugen and Stalagg remains the only pair of cards directly referencing each other. Even though it can be hard to pull off, summoning Thaddius in a blitz of lightning is its own reward.
Goblins vs Gnomes
Between its game-ending effect, awesome animation, unique (until recently) keyword and its very own theme song, Mimiron's Head has it all. Bask in the glory of the V-07-TR-0N!
Blackrock Mountain
Majordomo Executus goes in the footsteps of Lord Jaraxxus, replacing your hero with one of the most iconic legendaries (formery) of the classic set, this time as a deathrattle. Despite the transformation being a death sentence for you more often than not, getting to play as Ragnaros is simply too awesome to resist. DIE INSECTS!
Grand Tournament
This set saw a lot of interesting effects, such as Dreadsteed or Astral Communion and even the poor trash-tier Bolf Ramshield, but in the end I have to give it to Justicar Trueheart. The concept of upgraded hero powers have been used in other ways since, but back then it was quite cool to see a legendary have a different use depending on which class plays it. Tank up!
The League of Explorers
While all four members of the League (as well as their Nemesis Arch-Thief Rafaam) had unique effects, the best one was Elise Starseeker. Her battlecry started you on a journey to find a treasure map and only after that you had a chance to turn the rest of your cards into random legendaries. So much potential value was unheard of until then and as it happens, Elise was actually competitive card, seeing play in many a greedy deck.
Honourable mention goes to Reno Jackson, who brought the first deckbuilding restriction and made many a player rich indeed.
Whispers of the Old Gods
Any of the Old Gods would fit, really, but there's only one true God of Death, Yogg-Saron, Hope's End. Often dismissed as a joke card before release, Yogg turned out to be so powerful and swingy that eventually had to be nerfed. At least we still have his Puzzlebox.
One Night in Karazhan
The Big Bad of the adventure, Prince Malchezaar brought the first "Game Start" effect, shuffling five random legendaries into your deck, allowing you to start with 35 cards. And while this dilutes your deck and reduces your chances of drawing important cards, many a new player was happy to have a chance to play with expensive legendary cards without having to craft them. He's also a key element to the ever hilarious 35 legendary deck. Highly recommended, if you can build it.
Mean Streets of Gadgetzan
So many cards to choose from! From the unassuming Weasel Tunneler, through the dreaded Patches the Pirate (whose charge had to be patched out), the whole Jade mechanic and the concept of tri-class cards, in the end there are two cards that were truly worthy of this list:
Kazakus let you go through three "discover" phases to create a perfect spell for your current situation. While the effect could fizzle at times, the enormous value when combined with Brann Bronzebeard made it must have for any Reno style deck.
The best one was without a doubt Mayor Noggenfogger. This Mayor generated major chaos whenever he entered the board and went as far as to change your mouse pointer AND jumble emotes for each player, even allowing you to say to use the "Sorry" emote when it was eventually removed. Shame he died so easily to AOE damage, but anyone who ever played a game where more than two of these ended up on the board, we should be glad he never saw play in competitive decks.
Journey to Un'Goro
I'm going to pass on the obvious, since every single Quest card eventually gave you an amazing and unique reward and instead mention the return of Elise Starseeker from the League of Explorers.
Battlecry: Shuffle a sealed Un'Goro pack into your deck.
W... what?! Once you see it in action, the effect is not that special, but wow, I remember being just dumbfounded when she was first shown. Bonus points for the nice callback to the mechanics of her original card and the excited cry of the innkeeper after opening the pack, which also has a higher chance of giving higher rarity and gold cards than a normal pack would makes it a joy to play.
Honourable mention goes to Sherazin, Corpse Flower, utilizing the new mechanic of unremovable permanents first seen in the Karazhan single player.
Knights of the Frozen Throne
Let just start with the Death Knight cards. Reminiscent, yet not quite the same as Lord Jaraxxus way up at the beginning of this list, there are two that stand out in particular:
Uther of the Ebon Blade was the first card that explicitly allowed you to just win the game no matter what, provided you could fulfill a condition. Meanwhile Deathstalker Rexxar is a monster of a value engine with a completely unique effect
Meanwhile The Lich King (and Arfus) were Blizzard's nod to people wishing they'd add a Death Knight class. At least we got some spells and a kickass weapon.
Honourable mentions to the three princes who overcame their drastic deckbuilding condition and ended up all seeing play, even though most people considered them a joke before release.
Kobolds & Catacombs
Rin, the First Disciple is another card that starts you on a long journey, requiring you to play five five-mana Ritual cards. Then you blow up the opponent's deck with a 10/10 demon. While the reward is less powerful given the long setup time, just sending the opponents remaining cards flying everywhere was incredibly satisfying.
Honourable mention goes to King Togwaggle, who allowed you to trigger the PTSD of any League of Explorers veterans and just STEAL their remaining deck, though you had to work a bit to make sure they can't just take it back on the next turn.
The Witchwood
Another expansion with plenty cards to choose from. There's the humble Nightmare Amalgam which combines ALL minion types (and comes with awesome art to reflect that), Chameleos, who lets you peek into the opponent's hand and of course Shudderwock, a centerpiece of many quite degenerate combos. I'm going to have to give it to Toki, Time-Tinker, though. This feisty gnome allows you to reach back and time and play any legendary card that has since rotated out of standard. It's a shame that her unique effect will stop being interesting once she herself joins the wild.
The Boomsday Project
The triumphant return of Dr. Boom gave us Whizbang the Wonderful. Add this guy in your deck and... you're done. That's the whole deck. Giving you a random deck to play out of the current roster of deck recipes, Whizbang is a beloved card of many new players and the first card whose effect can be felt even before the game begins, in your collection. Craft him golden and you get a fully golden deck! Sadly it seems like Blizzard is not planning to add this card to the classic collection, though we did get Zayle, Shadow Cloak with a similar functionality.
Rastakhan's Rumble
The Corrupted Blood incident in World of Warcraft was one of the most memorable happenings in any MMORPG and as such it a no brainer to a callback to it in Hearthstone. Hakkar, the Soulflayer went through many iterations until the design team settled on the current one. Of note is how the Currupted Bloods shuffle more copies into the decks only after the draw is complete (unlike, say, Map to the Golden Monkey) in order to prevent the effect from outright killing fatiguing heroes.
Honourable mention: Hex Lord Malacrass is an very interesting card, giving an extra layer of strategy to the mulligan phase.
Rise of Shadows
One of the themes of this expansion was callbacks to previous sets, which might explain why there's not that many unique, let alone mindblowing effects. There is one obvious choice, thouhg: Swampqueen Hagatha, with her ability to "teach" shaman spells to a minion she generates, which then happen as a battlecry. Of note is the impossibility to chose more than one targetted spell, so that the resulting targetted battlecry doesn't sabotage itself.
Saviors of Uldum
I mean... there are the Quests. There's Mischief Maker. Mogu Cultist. But it's Zephrys. Of course I pick Zephrys.
So that's that. Defintiely makes me wonder what they're going to print in the future. If you think I missed any particularly interesting cards, feel free to argue about it in the comments. Oh, and thanks for reading (or at least skipping) this far!
tl;dr
Here I the cards from each set I consider the most extraordinary:
Lord Jaraxxus, Feugen & Stalagg, Mimiron's Head, Majordomo Executus, Justicar Trueheart, Elise Starseeker, Yogg-Saron, Prince Malchezaar, Mayor Noggenfogger, Elise the Trailblazer, Deathstalker Rexxar, Rin, Toki, Whizbang the Wonderful, Hakkar, Swampqueen Hagatha, Zephrys
Edit:
As I expected, I missed a lot of amazing cards. Some intentionally, some because I'm a dummy, so here's everything people pointed out belongs on the list. Thanks for the suggestions and keep 'em coming!
Stargazer Luna and Soul Infusion have a new mechanic where position of a card in hand becomes relevant.
The Soularium is a nice, novel effect.
Iron Juggernaut was the OG bomb-shuffler.
Flame Leviathan's effect sucked, but I can't deny it's originality.
Blood Of The Ancient One. I can't believe I missed this one. It's gold, Jerry, gold!
The Darkness didn't make the cut, since Sherazin I thought Sharazin was too similar, but the powerful presence of a 4 mana 20/20 cannot be denied.
Mecha'thun definitely deserved a spot. The instawin effect was previously seen with DK Uther, but the condition of "If you have no cards in your deck, hand, and battlefield" made my jaw drop when I first saw it if I recall correctly.