When I first started jump roping as part of my training and warm up, I could not go for very long and would be sore for a couple of days.  But with training and persistence, using the jump rope is one of those exercises I use consistently when training.  Most of the time, I use the jump rope in my warm ups, before going hard during my martial arts routines.  Jump roping is a great alternative to running and in some cases, may be more beneficial.  But, before anyone comments about their disagreements, it is not a replacement of running.  Anyway, there are some great benefits to using the jump rope.
Boxing, MMA, and seasoned martial artists use the jump rope in their training regimen.  They have used it for so long that it is second nature to them.  It is something they do so much, they could last for a long time.  Bruce Lee used it in his training to improve his overall fitness.
Benefits
When you jump rope, you develop a rhythm improving how you move when you fight/spar.  It also helps your cardiovascular endurance which is critical when sparring for any length of time.  Just as with running, using the jump rope increases lung capacity and improves your overall fitness.  I believe the most beneficial for me has been the ability to move more quickly when sparring.  I have more control of how and when to move, and the cardiovascular capacity to finish a fight.
Basic Tips to Improve Jump Roping
There are a variety of ways to start jump roping.  As you read further in this article, you will find a brief list of ways to improve your jump roping capabilities and improve yourself to be a more developed fighter.
Start jump roping.  Jump rope as much as you can for as long as you can.  If you can only go thirty seconds, you know where you need to improve.
Jump for one minute.  Set a timer for one minute and jump as long as you can.  Repeat this step 5 times for a total of five minutes.
30 – 30.  Your goal here is to perform 30 reps, 30 times.  So, 30 sets of 30 repetitions.
1000 Jump Count.  Jump rope for 1000 repetitions.  Count each time the rope hits the ground.  Go as long as you can until you have achieved 1000 reps. Your goal here is to do 1000 repetitions without stopping.
Conclusion
This is just a brief list of what you can do to improve your overall fitness using the jump rope.  This is not meant to be the final decision, but for those that are new to the jump rope, this should get you off to a great start.