If you are a runner suffering from achy or "bad" knees, first off know that you are not alone! "Runner's Knee" or pain in your knees that is exacerbated by running is a very common ailment among short and long distance runners alike. As a disclaimer right off the bat, bad knees are not something to take lightly and you should definitely see your doctor if pain persists after taking a few days off. We will get into some exercises and habits you can incorporate into your daily routine that will help strengthen your knees but if there is a serious injury (such as a painful ligament tear, partial tear, or fractured or broken patella bone, exercises might just worsen the condition and you will need casting or surgery to properly heal the knee).
First off, it is important to understand that "strengthening your knees" really means strengthening the muscles surrounding and supporting your knees because the knee itself is mostly composed of bone and cartilage, which unlike muscles and tendons, can't be directly strengthened. However, by focusing on strengthening your quads, hamstrings, IT Band, hips, and even your core, you will offer the knee more stabilization and be less likely to further injure it. Healthy, strong muscles around the knees also takes away the "brunt force" that the pounding motion of running puts on the knee, which is the most common reason for runner's knee in the first place.
To strengthen those quads and hamstrings, stick to the basic exercises that heavy weight lifters continue to hit home as being of top priority: squats, dead lifts, and lunges. We know. You're probably a runner and strength training, especially with heavy weights, probably is not your preferred form of exercise. But it is paramount in maintaining good running health. Even just a couple times a week of incorporating these exercises into your routine will show strengthened muscles. If you prefer more cardio-centric muscle enhancing exercises, try squat jumps, squat thrusts, mountain climbers, and walking lunges. And definitely get in some planks to stabilize and strengthen your core, which can help with your posture and ultimately will lead to better running form.