Some great answers here. I usually will pop in SMB3, Mega Man 2, DuckTales, Marble Madness, or NES Virus Cleaner to name several.
@MachineCode I too wish Marble Madness had a sequel.
As far as the ones that are just pick up from a save, if there has been a while between plays, I usually have to start over. This mostly applies to RPGs. However, @RH I agree with you about FF7. I have played it so many times, I can load a save, look at where I am on the map or in a town and know what I have to do. This also applies to Castlevania SOTN. Just open the map and go.