The Zelda saga - Follow Link's adventures on Nintendo Forever

Castlevania is a major video game series and, although it is a Konami game, it remains closely tied to Nintendo even though some entries came out on other consoles.

Castlevania 1 on NES

The founder. A classic action platformer, but back then, a banger. The controls are good, the difficulty is well balanced; if you care about the story, the game is worth trying.
A few videos:

Castlevania 2 - Simon's Quest on NES

Like Zelda, Castlevania changes shape with this Castlevania 2 (in many ways it is close to Zelda 2). A beautiful atmosphere, good music, a nice world... Too bad the dungeons are a notch below and a few puzzles are lame (at least my walkthrough will come in handy).
A few videos:

Castlevania 3 - Dracula's Curse on NES

The natural evolution of Castlevania. Its true sequel, in a way. More levels, branching paths, secondary characters. It was poorly rated in Super Power back then and I never understood why. This game simply deepens a proven concept.

Super Castlevania 4 on Super Nintendo

A sort of remake, but well disguised. In fact it is a new game with plenty of levels before you enter the castle through the gate. Even there you get a few nods, but it remains a completely different game.
A few videos:

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