If the keys seem to stick it is most often caused by Java needing more CPU power than your computer is giving.
Somethings you can do to help the games play smoother are:
1) Use the NES lite mode instead of Full mode. That would mean you would not be able to save which would suck for Zelda.
2) Reboot your computer. If you are playing a game in Java and close that game and then play a second game, the first game can sometimes leave data in memory that slows your computer down. Rebooting is a sure way to clear your memory. You can also just close all browser windows and wait 10 seconds and then open your web browser again.
3) Make sure you have the newest version of Java installed. You can find the link in my sig.
4) Disable sound. In NES full mode you can do that by pressing S.
5) Do NOT enable any extra graphic features found by pressing escape to bring up the menu.
6) Do not use the rewind button (backspace).
7) If you are using IE, try Firefox.

Close any other running programs such as media players.