Easier Asgore Fight
At the start of this game, Toriel will offer you a piece of pie. Save this till the battle versus Asgore, and eat hit in front of him. His attack and defense will significantly drop.
Easily Defeat Muffet
To defeat Muffet in a single turn, you can use one of the Spider Bakery items - the Spider Donut and Spider Cider - you can buy significantly earlier in the game. Use one during the fight and it'll end immediately.
Final Fantasy 6 Opera reference
The scene where Mettaton traps you and sings about your doomed love prior to sending you to the dungeon is a reference to the popular opera scene in Final Fantasy 6, especially the tune "Aria di Mezzo Carattere" sung by Celes.
Weaken Asgore
If you save the pie given to you by Toriel from the beginning of the game, and use it during the final battle versus Asgore, you will weaken his attacks noticeably; being relatively hard to dodge, this makes the battle significantly easier.