Disney Slytherins... I was about to say I wouldn't put Eugene in Slytherin, I was thinking maybe Hufflepuff actually, but he really DOES do anything to achieve his end (cuts off Rapunzle's hair to save her, despite his imminent death).
Let's not forget that she tripped over the same hair making her fall out of the tower that had always been there to pull her up the tower. She was literally killed by everything she treasured. Not by the girl she raised or this guy who just showed up. But the magic hair she treasured more than anything.