My best moment was the first time I beat the wall of flesh legitimately (I made the mistake in my first playthrough back in 1.2 of accepting endgame weapons from friends, making the game really easy and boring, so those fights don't count). The fight went something like this:
I had my bridge, waaaaay too long as always. Running across it, shooting at the wall with diamond staff, then phoenix blaster when I was out of mana. As he got to low health, I accidentally dropped through a platform into one of the obsidian towers and he caught up to me. He grabbed me, dragging me through the wall before I managed to get away with my hookshot. This, of course, put me UNDER my bridge. So for the last 500 health or so, I fought him by hookshotting under my bridge as fast as I could while shooting behind me. I have over 700 hours in Terraria and just today cleared expert hardcore for the first time ever, and that is still without a doubt the most intense fight I've ever had.
The worst moment is a bit trickier. My first thought was, when my friend came over one day he brought his world on a usb stick (we couldn't figure out how to do multiplayer back then), and that's where I got all the good weapons from. Once I got all the stuff, he went into the worlds folder and deleted 'world 1', which was the name of his world. Unfortunately, 'world 1' was also the name of MY world. So...yeah, my first world, gone. I quit for a while after that.
But in retrospect, this was probably one of the best things that could have happened. It really planted the regret in me for taking all those weapons and making the game trivial. It gave me a fresh start once I played again, which lead to that wall of flesh fight I mentioned. And that's what really secured it for me: when I beat him from under my bridge, watching him gain on me while I hooked and prayed, I realized how much you lose from an experience by skipping to the end. That whole 'journey is more important than the destination' thing is on to something.
So, worst thing....losing a post-golem hardcore character to a medusa in the shadows, while just using him to farm for resources for my main world. I didn't really need the character any more and was too scared to fight the moon lord in hardcore back then, but it made me sad to have lost him after so many hours.