Always 13, in every game. I don't like how any of the other eyes look to every other direction, or if they aren't looking sleepy or alarmed. At least with 13 it feels like they are looking forward and not fixed on a certain emotion.
1 and 9 are the ones I use for for my profiles. I don't like the newer eyes and I don't think I will ever use any other eyes. 1 and 9 are the ones I only use in any AC game. They look best.
On my first island, I went with 1, but on my second island I've gone with 10, the turnip eyes! Interestingly, they seem to be the two most popular styles.
This play through I've got 13, the bead eyes, just to try something different. I've now had them several months and I love the sparkle on them as well as how much color they've got. I think they look really friendly and cute, and just a touch doll-like. I especially like how they go with the curvy line mouth. In prior games I always did 1 or 10, but I don't see going back to those now that I've done 13. It's one of the very few things I never change about my appearance.
I think I'll play different characters on my island so I'll get more eyes options to vary the appareance. I love everything but 2, 3, 4, 5, 8, 12. So my characters will have other eyes. Probably 9 for my first character, but I definitely want 6, 10, 11, 13.
I'm not planning to change something else than haircut and colour for my characters. For one however, I will have to change skin color for a pale (white) one. Eyes colour as well I'll have to change as we can unlock more with Miles.