The Wii comes right out of the box with a great title called Wii Sports. In Wii Sports, you can play Tennis, Baseball, Bowling, Golf and Boxing.  Most of the games give your upper body, especially Boxing a decent workout.  There is also Training and Fitness modes that give you different ways to play the 5 games by presenting the user with different goals.  Workout With Wii presents several ways to modify your gameplay to give you a much better workout:

• Tennis - Tennis is one of the more popular and fun games in Wii Sports.  Most of the time during the Wii launch publicity, Wii Tennis was the game being demoed.  Moving your feet while playing is a great way to get additional exercise while playing tennis.  Better yet, move around like your actual Wii character on the screen.  The constant movement is sure to work up a sweat.
  
  
• Boxing - My personal favorite.  Practice your footwork as well as punching. Step side to side and forward and backward.  Most people I see playing simply throw punches.  Try bobbing and weaving.  Your Wii will move like you do.  And a special tip from a youngster who loves Wii Boxing - Dance around after you knock the Wii controlled boxer out.  You still have control on a knockdown so your Wii will dance with you.
  
  
• Bowling - Move forward like you are actually bowling in a real alley.  Also keep up the pace, no lolly gagging after each shot.  Be ready to go after each shot.
  

I try to play each of these games for 10 minutes straight.  After 30 minutes you are sure to have worked up a good sweat.

Additionally, try playing all of the games with your less dominant hand.  I am right handed but to switch things up, I play Golf and Baseball left handed (be sure to change your Mii as well or the controls might not work as well).  It's a good way to add some additional challenge to the games and also exert some additional energy. 

Note: Check out this article to see if you should consult a doctor before you start or significantly increase your physical activity.