Final Fantasy X

I can think of a few games I appreciated way more the second time around, but rarely will I give a game I hate a second chance. (That has happened though, usually with 'classics' that I thought I obviously just didn't "get" my first attempt. Surprise, my first impression is rarely wrong in this regard.)

Xenogears (loved the first playthrough, loved the second one even more), and Final Fantasy XII (hated the game my first playthrough, thought it was decent my second.)

Well not necessarily didn't like the first time, cause it was great still, but Xenoblade Chronicles, imo is way better the second time around.

Each of the cutscenes and various side quests in the game have so much more meaning when you've played the game already.

Too many to name to be honest. Most RPGs I like better on the second play through. Like a good movie, you notice a lot of details you missed on your second run through a good RPG. In the cases of RPGs with multiple endings or protagonists, you'll pick up things you didn't notice even after several play throughs.

Mario & Luigi: Superstar Saga.

I just mindlessly breezed through it as a kid.

On a second playthrough, I was able to enjoy things the game featured like the witty dialogue.