If I remember right, it was Zelda 1 back when I first got my Wii in 2006. I had/have the game on NES, naturally, but at the time my NES barely worked. After that I mostly picked up system gems that I didn't physically own, like some Megaman titles before I properly added them to my collection and Final Fantasy, which is still very absent from my physical collection.
On the Wii U, I grabbed the Metroid Prime Trilogy when it was on sale and then Mother 1 on launch, not because I cared to play it without the Easy Ring but simply to use my wallet to show my support for the series.