Game & Watch Gallery (GB)
To erase all the saved data on the battery, press Up Up Down Down Left Left Right Right on the title screen.
On the "game options" screen, press Select to toggle the music on or off. An animated note will be in the upper-left corner when the music is on.
During a game, press Start to pause, then turn off the Game Boy. When you turn it back on, you'll be able to start that game from where you left off.
Extra Hard mode
Earning 1,000 points in a "modern" game unlocks the extra hard mode for that game. Just press Up on the "game options" screen.