Leaving putts short (but on line) usually comes from a tentative stroke.  Trust that you have the line, and aim for the spot directly on the BACK of the cup, where you want the ball to lightly bounce OFF of on its way to the bottom of the cup. 

On the practice green, start with two footers, hitting the back of the cup, and then move back to 4 feet, etc. 

Whenever I leave putts short I always say to myself there is green behind hole (which most of the time there is.)  And I wont be afraid to pass it a foot or a foot and a half bye.

i saw a drill on GC from Michael Breed that was great. it was just taking the putter with no backstroke and pushing the ball like a broom to the hole.

Try picking a target about a foot behind the hole. Pretend like you are putting to that target and the hole will get in the way. Also, trust your stroke. If you are not sure about your stroke you will tend to leave it short. Also, practice on speed instead of line on putting green. it will help you align both together.

I take lessons from Crag Shankland, 2013-2014 Top 20 Teacher.  On putting he told me that the reason why my speed was inconsistent was because my putting stroke was the same for every length of putt.  Make sure that you are adjusting the length of your stroke for the length of the putt.  Will 100% make you more consistent.  Good luck!!

Leaving it short is frustrating for sure. The only way to get it dialed in is practice. I have heard some people split it up, 6 feet and in, then 20 plus - nothing in between. I think lag putting, long ones, medium ones. mix it up. I also like to do it with just 1 ball. Hitting it in the center of the clubface will give you a consistent roll. practice hitting it in the center by using just 1 ball and then going through your whole routine every shot. I think you'll get more out of that than hitting 10 in a row from one spot. If you change the shot every time, then you have to get the feel for longer or shorter - and you'll start reducing the ones left short too.

stick a tee parallel to the ground in the back of the cup and try to get the ball to hit that tee as it goes in

I think putting is what drives most of us crazy....

Distance Control....what is the best way to get that feel.  Certainly all of the tips that have been posted so far can help and you may find that one of the drills listed works very well for you and that is the key, what works for you.  Like you, I struggled with distance control for a long time (long and short).  I finally came up with a way of practicing that works for me and that transfers to the course very well...I just practice with one ball and try to put every putt in the +/- 1 ft range (not always perfect, but a good target).  I don't hit the same putt twice and I hit putts that vary in length and break each time.  I also make the second putt regardless of the length.  Granted, I still have long & short days, but nothing like I had in the past.  I also find that being on the practice green alone helps (no distractions).  Actually, I was out this morning practicing....practice green all to myself!

I know its "mechanical" but what works for me is to get on a flat part of the practice green and hit some putts where the putter goes from toe to toe. Do it from both directions a couple of times. This is now your "core" distance. Longer putts swing longer - shorter - swing shorter. As you look at the putt from the other side of the hole you can easily pace off the distance.

I find when I do this for the 1st few holes distance control become automatic after a while.

I had a putting lesson this summer and the pro i went to has a putting stroke monitor (think trackman but for your putter with sensors that you attach to the face and shaft) and i learnt so much about my stroke it was unbelievable.

One thing I learnt which reinforces what a lot of the guys have said is that your stroke should have a 2:1 tempo, with the through stroke being twice the speed of your back stroke.

I try to think of all my putts as par saving putts (including birdie looks) and that usually helps me get the ball past the hole. I don't like to think too much about mechanics or anything when I'm out on the course playing... so typically after I make my read, I just tell myself that this is to save par and that works for me.