Without out a doubt, the most memorable thing besides the characters, puzzles and items used in the Zelda series are the awesome boss fights. For each game, my favorite boss battles would have to be:

(original): Gohma. As easy as it was, I really liked how unique the boss was here.
(Zelda II): Thunderbird. Frustrating, yet surprisingly fun if the player knew what they were doing.
(aLttP): Blind the Bandit. Blind managed to change up the rules of the dungeon by having to actually lure the boss into the boss chamber if the proper conditions are met. That's when the battle begins, and I love Blind for that.
(OoT): Twinrova. I loved the duality aspect of the boss and turning their magic against the other.
(MM): Goht. Odalwa honestly freaks me out for some reason, Gyorg is unpleasant to fight and Twinmold is... Twinmold. Goht was the only one that was fun to fight against.
(WW): Molgera. Awesome music, and I really liked beating on its tongue after hookshotting it.
(TP): Stallord. My only regret was that the Spinner was a one-time thing only.
(SS): Koloktos. Loved how powerful the whip made me feel in this game.
(Oracle of A): Honestly, it's between Octogon and Shadow Hag. Shadow Hag was a brilliant fight that showed the player creative uses to injure enemies, and I honestly love underwater sections in Video Games in general, especially in this game (Reminds me of Dive from Gen 3 in Pokemon). Imagine my excitement when the sixth boss works exactly like that.
(Oracle of S): Digdoger. Magnet Glove was awesome, and it was used very well in that fight.
(Four Swords): The Plant Boss. It required the most thought out of the other bosses (Except for Vaati, but I don't like counting Final Bosses).
(PH): Eox. Generally, I loved how the control scheme of Phantom Hourglass was, and Eox was the most interesting boss to play against (Other than Bellum. I loved using Ciela's time abilities in that fight). I mean, the player controls a levitating hammer!
(ST): Skeldritch. The Sand Wand is my favorite item of all time (Despite being a one-shot too late for more use item), and this fight made me feel like an Earthbender. Benders from the Avatar series are awesome, so this fight is full of win.

original: Aquamentus. It's more about the feeling - every enemy up to this point has taken 1-2 hits to beat. Then there's suddenly a giant green dragon shooting a bunch of shots at you that isn't going down without a fight. That fight set the feel for the rest of the game for me.
LA DX: All of the Nightmare battles. It's difficult, appropriate for a final boss, and awesome because you're fighting back past foes. It gives you the sense that this thing is more powerful than all of those foes combined.
OoT: Haven't finished it yet, but right now it's Gohma because it was cool to see that old boss reimagined in such a cool way. King Dodongo is a close second for the same reason.
TP: Haven't finished it either, but I really love the Armogohma fight. It wasn't exactly difficult, but sent shivers up my spine and, again, reimagined good old Gohma in an interesting way. Plus, what happens after you defeat the giant spider...yeah.
PH: Crayk. That battle's mechanic was so awesome.
aLbW: Tie between Kucklemaster, because it was awesome, and Stalbind, because it had fun mechanics and a challenging fight.

From the games that I own:
Minish Cap: Vaati. Seriously, Minish Cap has the best Vaati fight out of the series.

Twilight Princess: Dark Lord Ganondorf. Admit it, TP had the best Ganondorf fight.

Skyward Sword: Tie between Ancient Automaton Koloktos and any fight with Demon Lord Ghirahim.

Phantom Hourglass: Diabolical Cubus Sisters. I honestly remember them more from the other bosses, so that's really all they have going for them.

Spirit Tracks: Cragma. It reminds me a lot of Stallord, but to me, Cragma just felt like a cooler boss. Ironic since he's lava .

Ocarina of Time: Ganon. Just...Just, Ganon. TP may have had my favorite Ganondorf fight, but not Ganon.

Wind Waker: Tie between Molgera, Kalle Demos, and the Helmaroc King.

Link Between Worlds: Stalblind. I thought the strategy to beat him made a good use of the Merge, which up until then was just used for travel and solving puzzles. Also, am I the only one that thinks Stalblind and Death Sword are somehow related?

So far:
OoT: Volvagia. His story was so sad if you read the manga and connect the stories to each other...
MM: Odolwa. He was just plain weird. Kind of like me.
WW: Molgera, hands down. Greatest Zelda boss music ever. (Greatest boss music ever period is The 13th Struggle, the theme for all of the Organization XII boss battles in Kingdom Hearts RE: Chain of Memories, except Marluxia. Greatest Zelda music ever is the Hyrule Field theme from Twilight Princess.)
TP: Fyrus. Another touching story, given that Darbus seems to feel true remorse for his actions.
SS: Koloktos. Loved how the Whip was almost OP in this battle.