In the combative arts, it seems logical that punching harder would lead to increased effectiveness. But is this skill trainable, i.e. can things be done that lead to increased punching power?  The authors of “Increasing the Impact Force of the Rear Hand Punch” think so.  They (Turner, Baker, & Miller; Strength and Conditioning Journal, Vol. 33, #6, Dec 2011) identified 5 trainable qualities that influence the impact force of the Rear Hand Punch (RHP):

1. Increase rear leg drive
2. Following the step forward, land with a rigid leg
3. Increase the stretch-shortening cycle (SSC) of the trunk musculature
4. Increase the velocity of the punch
5. Increase the effective mass

To train #1, they recommend using exercises such as the squat, deadlift, & clean, as well as plyometrics. The second attribute (landing with a rigid leg) is meant to increase braking and transmission of forces. Their recommendation is to use plyometrics that emphasize the landing element.  To train the SSC of the trunk, medicine ball training can help with the development of rotational power.  To increase the punch velocity, ballistic exercises such as plyometrics including medicine ball throws and Olympic lifts are recommended.  The key here is ensuring acceleration thru the entire movement. And to increase the effective mass, it is strongly suggested to use pad and bag work that incorporates impact (vs. non-contact sparring or techniques in the air).  
One thing the authors mention is that the punch is initiated by stepping forward.  While this sequence may lead to increased punching power, it is potentially slower and more
telegraphed than when the hand/weapon initiates the movement.  This “true timing” (hand/weapon, then body, then feet) from classical fencing is the ultimate goal in a weapons based system, since the resulting
effectiveness relies on the speed of the movement and impact/piercing of the
weapon as opposed to maximum force.  The opponent can be struck before they’ve even realized that a motion has been initiated, let alone before they have time to respond. 
A subtle point, but one well worth exploring further if you’re a weapons-based player.  
So, back to the punch.  Bottom line is that to increase your punching force, work some fundamental and explosive movements into your training regimen.  Squat, Deadlift,
Clean, Snatch, Plyometrics of many kinds, KBs, Medicine Balls, and Sand Bags would all work great.  Be creative, and as always, have fun.

Great article by Rob Panariello over at the 8 Weeks Out site  that raises an important point - how much strength do we really need for our chosen sport?  On any given day the stronger and faster athlete should do better at an activity compared to someone of equal technical ability. But there is a limit on how much time should be spent on increasing the reps, weights, sets, times, distances etc. at the expense of technique training.  

My sensei always said “if you want to get better at karate, do karate”. His rule of thumb was that cardio and strength training (in that order) should come AFTER you’ve spent time refining your basics, kata, sparring, and pad/bag work, not INSTEAD of that
technique work.  It should be a balance, but if your chosen sport is karate, don’t lose sight of that fact and get wrapped up in becoming the next CrossFit games winner on ESPN.  Get in enough shape, but as Sensei Dorow once said: “Someday someone will
challenge you.  If you are not technically proficient, you will be destroyed.”