I totally agree with Final Fantasy V and VI as well as the Paper Mario games mentioned above. These games definitely deserve to have a great return in a more modern style, but of course keep the games mostly the way they were.
If I had to name a few outdated games that deserve to be re-made, I would have to say:
1)
Banjo-Kazooie: Hands down; one of the most entertaining, addicting, and challenging games of all time in my opinion. Seeing this on the Nintendo 3DS would keep me going for hours on end each day! Such a memorable game
And, since I mentioned Banjo Kazooie, I might as well mention the sequel:
2)
Banjo-Tooie: Even though I, as well as many others, love the first installment the most, this sequel was phenomenal and memorable. With the challenges this game had, this definitely would go interesting to see return......with interesting additional challenges, etc.
3)
Donkey Kong 64: Easily one of my favorite Donkey Kong installments. I always loved the style, gameplay, challenges, differentiation between each character, and levels.
I can name many more, but I'll a narrow list such as the one above