The first demo I really played on my 2DS was Bravely Default... I really liked it a lot! +I got extra stuff :3 I didn't have a lot of other games to play at the time, so I just never closed the software to avoid the use count and played it for days.
..then I got the game and after like chapter 5, the job grinding chased me away from it ;w;
Otherwise, eum, PMD: Gates to Infinity, Etrian Mystery Dungeon: IV, and MH4U were demos that I all liked--but the MH4U demo didn't tell me that there was so much character customization in the full game ;w; I didn't even know that there was so much more in the real game.
Yokai-Watch was.... I could tell it was a very good demo, and it didn't have a lot of handholding, but it wasn't my type of game. A little short compared to the other ones, though, with about half an hour of gameplay if you don't explore everything.