No motivation - If you're used to running then motivation is something you don't normally lack. You're used to running on a very regular basis and are used to the feeling it gives and want more of the same. Running may come naturally to you and you look forward to doing it. If you're not so keen as you normally are to begin your run then you could be over training.
You're frequently ill - This is a definite unmistakable sign from the body. Fit and healthy people normally have good immune systems, you shouldn't generally suffer from many illnesses at all. Over train though and you may start getting a lot of colds, you may start getting sick. You may get illnesses that your body can usually deal with but they affect you more, then you need a rest.
Low energy - or if you're feeling tired a lot. As runners we're used to feeling like we have all the energy we could have. Our bodies are used to providing us with lots of energy in preparation for our workouts. We feel high in energy while running and outside of running. When you're feeling tired a lot it's your bodies way of telling you to give it a rest.
Too much weight loss - When you uptake your running regime you need to do the same with your energy intake. If you're burning those calories they need to be replaced. If you're looking to lose weight then stop dieting once you reach a healthy weight. You need some fat because they protect your organs. Monitor your weight regularly and do something about it if it goes too low.
High resting heart rate - The heart rate will also be higher than it normally is when exercising. Fit people normally have a lower resting heart rate than people who don't exercise. Fit people can be in the range of 50 to 60 where non exercisers would be around the low 70's. Get used to monitoring your heart rate as it gives clues about how well you are as well as if you're over training.
Shin splints - I know I've had the feeling. When you run too much you may start feeling an aching pain in your shins. I've still had this feeling on a nice soft treadmill deck. There are tiny little fractures that can occur if you keep running with them making it worse. The only thing you can do is have a recovery day or two to let your shins heal.
Muscle soreness - This one even has its own name in the medical community: Delayed Onset Muscle Soreness (DOMS). They don't really know what causes it but after a strenuous day of exercise like a long run. The next morning you feel a soreness in your legs. This goes away after a day or two but if you keep running you can make it worse and make other injuries more likely to occur.
Over training is just something to keep an eye out for when you up your running mileage or intensity. It's easily done and very subtle as we've already said. Treadmill running everyday isn't necessarily too much but if you don't feel like running on a particular day then a day off won't harm your progress as you train.
Over training is a lot easier to do if you're weight training as the body needs time to recover from that kind of exercise. Treadmill running is easier on the joints but it's still possible to over do it. I personally monitor my heart rate and I'm fortunate that I haven't over trained yet. That will be the first sign for me and as long as I keep enjoying it, then I should be ok.