Maybe these are not strictly cutscenes since you can move around and control your character while they happen, but they're the introductions to their respective games more than actual gameplay, so I'll talk about them:
Evoland 1 - You start and this is the first thing you see:
You can only move to the right. When you hit the chest it opens and it unlocks the left key. You can then go to the left and open the other chest, which unlocks the up and down keys. It's in my opinion an awesome way to introduce the game's controls and the mechanic of opening chests to evolve the game.
Pokemon Reborn - The bomb, the torture scene and the atmosphere of Peridot in general are shouting at you that this isn't a regular Pokemon game. Reborn was the first fangame I played, previously I had only played Emerald and Pearl, so this beginning was certainly shocking, and it caught my attention since the very first moment.
Undertale - The contrast between the presentation Flowey makes of the Underwold, trying to fool you with the "friendship pellets" in order to kill you and get your soul, shouting that here is killing or being killed, and right afterwards Toriel showing you a radically different game where you need to talk to the obstacles to beat them shows the player both the pacifist and genocide routes without even talking about them. It also makes you instantly interested in the game and the different possibilities it may have depending on your choices.