I wake up at 3:30 a.m. most mornings & go running on the road and on trails. Have been doing this for a few years. I used to just carry a handheld until I started testing headlamps. Running at night with a headlamp is definitely the way to go, and is much more comfortable than always carrying a light in my hand (although I still carry one in my pocket as a backup light or as a throwy light.)
Some have mentioned 3xAAA headlamps with battery packs on the back of your head like the LED Lenser H7 (have one) and I really do not like this set up for running. Just too much to wear around your head. The H7 is a decent light, but there are much better lights & much better quality. The 3xAAA Petzls are nice to, but again too much to wear around your head.
For a couple of months I used a fenix headband, and tried running with a light on the side of my head. The fenix headband is nice, but too bulky. I then, with a lot of success, used a Nitecore head band with a regular flashlight worn on top of my head (there is a strap that goes around your head and one on top of your head with loops available for a light either on the side of your head or on top.) I mostly used a Quark AA or a Quark 123 or even a zebralight SC60 running a Li-ion battery for lots of output options and when needed lots of lumens (200+ in the quarks and 270 in the ZL.) This worked very well, and the lights riding on top of my head did not bounce around. Heavier lights, like a two-celled light, would bounce though, and were impractical to wear on my head anyway.
Earlier this year I bought a Zebralight H51w (neutral tint) and then a H51 (cool white.) The H51w was a huge improvement over what I had tried in the past, but I felt the neutral tint just did not give me the contrast I needed (seemed too dark,) so I bought a H51 cool white. The Zebralight H51 cool white is as close to a perfect running light that I have come across to date. The output levels are excellent, the UI is my favorite, runs on a single AA (eneloop is best,) with great runtimes, and is very lightweight. You cannot use the headband provided though as it is too bouncy when running. I use a NiteIze head band that I got at batteryjunction.com ---
Click Hear This headband is only $4, and is made of nylon. It is stiff and is very comfortable with no bouncing around at all. The picture on the website shows the guy wearing a light on the side of his head, but with a ZL headlamp you can wear it on your forehead since the light is angled. The zebralight headband is stretchy which is why their lights bounce around with their headband. The NiteIze head band is stiff nylon, and fits on your head with the comfort of a hat rather than a constriction band (constriction bands give me headaches....no thanks.)
Also, get the regular Zebralight not the floody ones for running. Some have mentioned running with a flood light as a headlamp, and that is just not a very good setup IMO. If you are running with a really floody light then you will be forced to run the light at the higher levels at all times because the light just will not reach out very well for you to see (especially on trails.) Running a flood light on max still just doesn't allow me to see far enough ahead. The ZL H51 has pretty good throw, and is perfect IMO for running. I can comfortably run it on medium when on streets and on the second high (H2 - 100 lumens) when on paved trails. And, when I'm on unpaved trails I then prefer the max setting to see well.
I have been using the H51 now for lots of things including camping, and just love it. My wife & kids love using them too. I am now really looking forward to the new Zebralight H600 which runs on a single 18650, and will run 170 lumens for 7 hours with a max output of 750/420 lumens! I am hoping that this will be lightweight enough to run with, and believe it will fit in the NiteIze headband....we will soon see. But, for an awesome headlamp that runs on a single AA, the ZL H51 is outstanding.