Melee:
The Terrablade.
You basically assemble this piece by piece, throughout the whole game, and while I feel it kind of got shoved to the side with the Martian Madness update, since the Influx Waver is about equally powerful (depending on who you ask) and is a LOT easier to get and cheaper to upgrade, this is still a great weapon.
High damage, you can move around and swing freely left and right, it has auto-swing, it has a ranged attack; the lot.
All my melee characters have one and even used it to take out Duke Fishron (until I get his flail).
But it's even more than a weapon. It's an icon. It reflects the journey you made, from defeating the Eye, visiting the dangerous jungle and underworld, raiding the dungeon, all the way up to defeating all three mechanical bosses and defeating Mothron. (Although I got a LOT of broken blades in earlier versions, where swamp guys dropped them.)
Even though I don't like running into yet another 'True Terrablade' suggestion (the name is far from original), I do get why people would like to see this sword upgraded and I share this desire. It'd have been very nice if you could have kept upgrading it throughout the game, eventually creating a ridiculously powerful sword with Luminite.
It's the only weapon that you keep upgrading, that's there with you until the end (until the Martians kinda ruined that).
There are a few weapons that can be upgraded once, but the Terrablade is quite unique here in that it contains so many parts.
I'd love to see something like having it charge up while you kill things, glow more and more green, and have it discharge with the right mouse button, striking dead everything currently on the screen (except bosses). It's a nice thought.
Ranged:
Tactical Shotgun.
No long story here. I like shotguns in games. I like to walk straight up to an enemy, release that shell and have whatever's at the other end of the barrel turn into chunks.
It never gets old for me to unload the shotgun in Terraria, seeing my dismantled enemy fly away from me faster than it ran towards me, thanks to the gun's high knock-back.
"Jeez, Gotcha, you psycho."
Haha, no worries, I don't share the same joy in real life. I absolutely hate guns.
Magic:
The Last Prism.
When I finish a game, I like to get something incredibly powerful, something that pretty much makes the whole game easy as pie afterwards. Something all players deserve after all that hard work and frustration. The game recognizes you climbed that mountain, overcame your weaknesses, grew with experience, finally reached the top, and rewards you with a gift from the gods, to make the rest of your continued play a pleasant holiday... if you want to.
And I want to. I love to have that one weapon in any game that makes me feel like a god, that pretty much smites down anything the game throws at you, and for Terraria this is The Last Prism.
It can clear out throngs of enemies in the blink of an eye, kills bosses in seconds, and with the right setup you can even pretty much god-mode through Expert Moon events, completely annihilating even the ridiculous amounts of Pumpkings in the Pumpkin Moon's final wave.
It was either this or the Inferno Fork. I like massive fireballs that pretty much kill any enemy it comes into contact with (and not just in Terraria).
Very satisfying to use. So a special mention is deserved.
Summoning:
Raven Staff.
I'm usually the good guy in games and generally don't inflict terrible things onto virtual characters, although sometimes I let myself go and do an evil walk-through of, for example, Fallout 3. Or play Dungeon Keeper. Sometimes it can be fun to be a bit wicked.
And as far as wickedness goes, I don't think any weapon in Terraria can beat the Raven Staff. A raven doesn't fight nobly with a sword and shield in its claws; it picks out your eyes and tears at your flesh.
So having a swarm of these go about the battlefield on their own, picking apart poor helpless enemies... yeah... that's... kind of special, isn't it?