This video shows all simple, non-conditional, neutral (pacifist) run, changes that come with reloading the game. For simplicity, this video only contains reload alterations done on one run, which means that reset changes aren't included (such as Flowey dissapearing after a genocide run reset), and it doesn't include all conditional reload changes (such as killing Toriel then reloading and sparing her, getting a speech from Flowey). Strangely, Papyrus will act like he knows you even if you reload one second after meeting him.

Fun fact: If you use a process monitor on Undertale, you can tell every time it calls a write operation (i.e. every time it actually saves). Examples of when Undertale saves normally:
Every time you save the game with a save point.
Every time you load your save file (it writes to playerachievementcache.dat, even if nothing changes)
Every time you die, it records your deaths. This is used for the resturant scene with Sans in the game, which is not included in this video.

There are a couple of other times the game writes files I didn't include because the results were too minor or I couldn't figure out what they did:
In the area before the final corridor, if you reload after hearing everything the monsters have to say about the royal family, the next time they talk, you will be able to advance their text with x or shift. You couldn't do this before.

If you save after you defeat Photoshop Flowey, but before you decide to fight or spare him, the game will skip to the fight or spare screen the next time you start it up. Reloading after choosing just takes to the screen after you chose.

The game writes output every time you use an elevator. I have no idea what this does.

The game writes output when you pull the northern switch in the corrider (the one that opens "The End"). I have no idea what this does.

The game writes output for every Mettaton encounter after the quiz show, but before the musical. I have no idea what this does.

The game writes output when the credits start in the neutral run, but before Sans' phone call. I have no idea what this does.