Super Mario Bros. 3

.You have the beat the game in one go, as there are no saves, like Tempest of Shadows already stated.

If playing on the actual Nintendo you can not save, if using an emulator on your PC you can go to file/save state as

You cannot save.

The SNES compilation of the Super Mario Bros. NES games allows saving. The NES version does not.

In the original NES that you are playing, the game can not be saved. You must play the entire game in one sitting. Only in Super Mario All-Stars for the SNES, and Super Mario Advance 4 for the GBA are the one's that you can save your game on. The Wii Virtual Console version allows you to suspend the game until further played.

The original NES version cannot be saved, as battery backed cartridges were a very new thing back in the late 80's, and didn't become common until the SNES era.

The SNES SMB collection titled "Super Mario All-Stars" allows you to save your games. The GBA version titled "Super Mario Advance 4: Super Mario Bros. 3" also allows you to save. The Wii Virtual Console version can be suspended.