The Legend of Zelda: Oracle of Seasons

There are some rings you can only get in Oracle of Ages and some you can only get in Oracle of Seasons. Whenever you get a new ring in either game, you can get a new password and enter it into the other game to get the new ring in that game also. Each game has a ring that can only be obtained by playing that game in a Game Boy Advance. You can also transfer these rings using the password. Be aware that you won't get the ring called Become Something Else if another file on your gamecard already has that ring. If this is the case, then you should probably finish the game that includes that ring, then transfer it to the other game via the password.

Yes it is possible to own all the rings at once but not the way this guy is talking about. You can do that for the most part, however some only show up in certain linked games so you would need to use the link cable to give rings to a linked game from a different linked game (LOoA->LOoS).

Yes, you get them using the gameshark code. See
www.gamefaqs.com/boards/genmessage.php?board=472313&topic=52860985
for more details