Nintendo likely has a very specific mass market idea in mind for the new device, but I have no idea what they have brewing. That won't stop me from speculating how I would like to see it in the games I play! Continue after the jump to read my simple ideas.
Trauma Center: This would be the perfect way introduce the peripheral in my opinion. Imagine that the calmer you are the easier and more focused your objective is. When you start to get antsy and worked up the screen starts to shake or something to that effect.
Horror Games: Anyone who has played the original Manhunt game on PS2 knows how much the headset added to the experience. You had to literally be silent as possible so enemies could not hear you. Now, imagine that type of game play gimmick added to your favorite horror games with your pulse monitored. You have been implanted with some type of bomb in your heart and you have to keep your heart beat down/up or it will blow up. Who knows, the possibilities are actually exciting when you start to think about it.
Rhythm games: I haven't quite ironed this idea out but I'm sure your pulse would make a great base for some type of rhythm game. The faster the beat of your heart the harder the game is . Imagine a "bit.trip heart beat"
I'm sure it will eventually be used as some type of WiiFit plus add on, but the hardcore gamer in me has some hopes it could actually be used to make games more exciting.