I've only had knee pain once from running, and it was a day when I had three strikes against me: 1) running in warm, humid weather and missed the first water stop so I got a little dehydrated, 2) I increased my mileage rather abruptly, and 3) my shoes were wearing out. So now I know that paying attention to hydration and proper foot gear is important.
It turned out to be an IT band problem, but it was pretty minor -- I rested it for a week, eased back in slowly, and got one of those roller things. This was last fall, and so far in this training season, I've had no big problems.
I'm just the opposite of you -- any discomfort I've ever felt running has been in my left side. I kind of expect this since I have scoliosis and one leg is about 5/8" longer than the other. I occasionally get cramps in my left hip, and that is my signal to ease up -- run slower or take a walk break. In fact, the day I felt that pain in my knee was a day I had been getting those warning signs from my hip that my left side was unhappy.
I remember learning somewhere that knee problems may be helped by strengthening the hip flexors, so Mo's suggestion makes a lot of sense to me. One thing I think is helping me recently is that I have resumed regular yoga workouts. Sometimes I'll take a yoga class right after one of my short (3 mi) runs, sometimes I'll alternate so that I run one day, take yoga the next, etc. I only run every other day, which helps my body to rest and heal.
Sorry to ramble a lot here! Just throwing some thoughts and observations out there. If this is ongoing, I would see a sports medicine specialist. One of my teammates fought through her shin and knee pain last June to complete a half marathon and is now *still* recovering from surgery to correct the damage that was done.
I do believe pain is our body's way of telling us we're doing something not quite right. I feel like a wimp sometimes because I'm kind of a slow, cautious runner (I'd love to get to where I can sustain a 10-min mile for more than a mile but it may not happen), but I'd rather be a slow runner who can run for 40 years than a fast one who gets hurt and has to stop.
Good luck!