Here are some I found out.
Those are all spoilers, obviously.

-If you attack and miss the dummy at the start 8 times, it has enough of your shenanigans and flies away.

-If you call toriel "mom" and then flirt with her she will comment on that and... remember it.

-If you keep humming to shyren until the battle ends, you will sing shyrens song to knight-knight and it takes 1 less turn to put her (?) to sleep.

-You can walk to the waterfall savepoint while one of napstablooks tunes is playing to get an unique encounter.

-Skip all dog-related battles by using the stick.
Yes that includes the dog in the true lab. Thank god.

-Mettaton will comment on you not stepping on a green tile that makes you fight a monster (him) in the colored tile puzzle... and then attack you anyway.

-You can throw the stick and equip the tutu in mettatons battle for extra ratings.
There are probably a lot more hidden rating raising items besides the obvious fastfood (glamburger, steak etc) ones.

-Skip muffet by eating a cheap spider item from the ruins in the battle.
Alternatively you can buy a spider item in hotland for 9999g after which the battle won't even start (haven't tested myself yet).
Great if you're like me and don't enjoy tapping "up" on the controller a lot during the pet sequences.

-You can weaken asgores attack and defense by eating toriels pie in the battle to make it a bit easier so he doesn' take forever when you hit him for no damage whatsoever with your pacifist noodlearms.

-At the end of a pacifist run, you can meet asriel at the start of the game if you don't quit and reload.
He'll have some interesting things about the fallen child to say.

(Spoilers, naturally)
If on your first clear of the neutral game prior to a true pacifist ending, spare Asgore but kill Flowey. After the ending, reload and do the fight again. This second time, when you spare Asgore and he finishes his usual text where he all but admits he wants to adopt you... he changes his mind. He says it's just a fantasy and impossible, that you remind him of his first human foster child, but that you are so full of hope. He tells you that he so badly wants monsterkind to be free, then deals the finishing blow to himself, and in his final breaths, he shakingly apologises for placing the burden upon you, but asks you to find a way to give monsterkind their freedom while you are on the surface, and hopes that you will find a way to foster a new peace between the races. He then expires, and Flowey does his thing before you can hug his soul.

It's a shame Asgore didn't get more gametime, though I suppose that's natural for an endgame character. Like Toriel, he seems simple and naive, but it's just a pleasant front that covers over all the more intense, complicated stuff underneith. This is why it kills me that the true ending never explicitly states whether or not they got back together, or whether Asgore resigned himself to just being near her. Which sucks. The mistakes that were made came from all the Dreemurr family, though Asriel gets a free pass given the awful ordeal he had to endure as flowey.

Hnngh.

On genocide in the Lab if you check the video feed that monitors you , the char will say " it is me ( charecter name ) " on pacifist it will say " is it me ? " Also the bag of dog food is half empty on genocide and half full on pacifist

At the rainy hallway in waterfall, if you start walking without an umbrella, the monster kid assumes you can't hold an umbrella either and starts walking with you. If you then go back and get an umbrella, she says "Yo! You got us an umbrella? You're the best!"

There's a fourth frog in that room in the ruins. If you examine the wall in the right spot, you find an ant sized frog in a crack.

If you tell the frog that you don't like yellow names, he'll offer to get rid of them. If you then talk to him again and say you want them back, he says that everyone already threw away their yellow names, but they still have last year's pink names they can use instead. For the rest of the playthrough, monsters you can spare have pink names. Later on, if you examine a garbage pile in the trash heap, it'll mention there's a pile of yellow names.

In the room where Sans pranks you with a telescope, examining the southern wall says
(The gems on the southern wall shine in a spectacular pattern.)
(It's a nice thing you can see the southern wall from this angle.)
Undyne also mentions it if you call her in this room

Running away from the training dummy in the ruins gives you an amusing message from Toriel. If you then walk past the dummy in the garbage zone without looking at it, he says it's just like you to run away

When Papyrus explains the tile puzzle, if you say you didn't understand he'll get them mixed up the second time around. If you say you still don't understand, he'll leave without doing the puzzle.

Originally posted by chris:

-Mettaton will comment on you not stepping on a green tile that makes you fight a monster (him) in the colored tile puzzle... and then attack you anyway.

- If you instead complete that puzzle, Mettaton will turn off the flames and prepare to attack you, but Alphys interrupts the battle for a moment. "Flames, deactivate!! ... huh?" "THE HUMAN FINISHED THE PUZZLE. I ALREADY TURNED OFF THE FLAMES."

- Trying to backtrack out of the Snowdin puzzle rooms without solving those nets extra dialogue. Here's the one for the word jumble: "SANS!!! THE HUMAN IS ESCAPING!!! YOU MADE THE PUZZLE TOO HARD!!"

- Inaccessible Echo Flowers have some weird dialogue. About being lost in the dark, begging for help, etc. Dunno if that's Gaster speaking, or maybe one of the humans who died there.

- You can throw Undyne's letter away. Then go back for a replacement. And she doesn't even mind too much, because she already wrote a better one. (The second letter is too 'powerful' to drop.)

- If you actually try to dance during the opera scene (either by running all around, or staying close to Mettaton), they will comment about that.

- Sans refuses to sell you more hot-dogs after your 30th one.

More of an unthing. petting lesser dog twice results in no snow creation. petting it three times led to snowbominations. seems theres no middle ground. Either it's not enough or too much.

Oh wow, that half-full/half-empty thing with the dog food is delightfully minimal.

in genocide mode, a lot of the bosses have several turns worth of dialogue, even though you can kill them on the first turn.

There are some nice game reload shenanigans.
Just after Toriel asks you if you prefer Butterscotch or Cinnamon, reloading the game will make Toriel say "Wait, you like [choice], right?" Saying yes will lead her to say something to the effect of "Ah, with every human that came here, I felt like I knew them for so long, it was like meeting an old friend.", commenting how she remembers some stuff between saves and how the other humans could also save.

Doing the same with Sans on a Pacifist run, that is, meeting him on the hallway, watching his speech to the end, then reloading the game will make him tell you a secret code. You reload the game again and again until he gives you the key to his room. There are a bunch of things there that only really make sense if you do the Genocide run.

Dodging Flowey's pellets will make him upset at first, do it for a while and he tells you to run into the bullets. He stops, looks to his speech bubble and rewrites it to "friendship pellets". Dodging them again makes him mad, he says that you DO know what's going on and that you want to make him suffer again. You monster.

Killing yourself on Omega Flowey's ring of bullets during his speech enough times makes his visor revert back to regular Flowey looking annoyed and he will say "Can you stop that?"

Throughout the game, you will find mice, food stuck to tables, and save points in the same location. During the walkaround stage of the True Pacifist ending, you'll find that the mice finally got to the food.

Additionally, if you kill Toriel and then reload the game, both Toriel and Flowey will comment on this. Similarly, if you shake Sans' hand and then reload the game, you'll shake his hand before he tells you to. Almost "like you knew that one."

You can take an umbrella back from the can and show it to Sans and others for additional dialogue. You can't take it over the ferry, though, so it's a little locked.

Papyrus often has more than one phone conversation for each room if you call him.

Also, try using the instant ramen from Alphys's lab in battle.

-If you attack and miss the dummy at the start 8 times, it has enough of your shenanigans and flies away.

Something similar happens if you constantly try to go downstairs. After awhile Toriel will give you the same look she did when you bored the dummy.

On pacifist routes, Sans winks his left eye which is the eye that flashes during his fight. In genocide mode, he winks with his right eye, meaning that he's not taking his killer eye off of you.

sorry if you're reading this /u/HighwayWizard

During the Mettaton musical, the game's title changes to UNDERTALE the Musical.
http://prntscr.com/8p8bxt

Sans calls you a freak if you fight him after killing him before.