One of my favourite NES games is Crackout, a Konami game (disgtributes by Palcom) that I used to play and be bad at as a child. It's a relatively simple Breakout style game (relatively simple compared to what crazy creativity got hold of game programmers since then when reinventing video game classics). Sometimes you have to destroy non-blick objects, like glass boxes or monsters. Often there are creatures that produce a variety of bonus objects that can help not at all or very very much when you collect them (depending on the situation you're in and what bonus it randomly produced).
One thing that I like a lot about it is that it has an interesting way built in to save games. There's no RAM on the cartridge. Nintendo games didn't usually do that in the early 1990s. Of course no flash storage, either. Rather it generated a string of characters every time you lose your last ball. This generated "Password" contains the level you were in as well as any other relevant statuses. When you start a new game you can choose to start from the beginning or to enter a password. Either way you always start with 6 balls. This means as long as you write down the password after a Game Over, or not turn off the console, you can always continue by starting again at the last level you were at.
I'm still bad at this game. But it still is fun. The levels get pretty challenging early on, which makes the priciple that you can only fall back to the beginning of the current level a welcome design choice. And because of the password system I can continue my recent appempt at advancing to higher levels than I've reached as a child on any console and cartridge I like, including emulated ones.
Edit: As I learned today, this method of letting the player continue at the beginning of the level at which the game ended, is actually pretty common for games from that area. Bomberman 2, for example, is even a game that I played a lot myself in my childhood, but didn't remember the codes about.