It might not seem like it now since so many of us have played it to death, but the original Super Mario Bros. is a tough game until you have the whole thing memorized, so if you're new to the game you're going to see this a lot:
But all is not lost! Once the title screen pops back up, hold down the A Button and press Start to start back up at the beginning of the world where you bought the farm.
Of course, as you get better, you probably won't need this any more. At least, that's the goal.