I run on a treadmill (about 11-minute mile pace) and use a heart rate monitor. I am 42, weigh 127 pounds and am in good health. According to the heart rate monitor manufacturer, I should work out between 117 - 151 beats per minute. I have read many different articles that recommend different heart rates, even up to 170 beats per minute. At a comfortable pace, my heart rate stays at about 155 - 160 beats per minute. What is the best heart rate range for me?

About your heart rate: There's no single right answer, which is why you're seeing so many answers. The standard formula for estimating your maximum heart rate: 220 minus your age. Some people prefer to work out at 60-65% of their maximum heart rate; others like to have more strenuous workouts at 80% or even close to 90% of max. If someone is writing for an audience of athletes, they'd suggest higher heart rate goals (typically 75-85% of maximum than if they're writing for ordinary people who just want to get some exercise to improve fitness and health (60-75% of maximum).

Let's take a closer look at your situation. Since you're 42, the formula (220 minus your age) gives you a maximum heart rate of 178.
60%=107
80%=142
90%=160

Assuming you don't have special health issues, if you can carry on a conversation while you're running (it's okay if you're breathing moderately hard), and if you feel good during and after, you're probably not overdoing it. If you're getting your heart rate all the way up to 155-160, you're exercising at the higher end of the intensity scale, into athletic training. That's fine - provided you aren't injuring yourself. Research shows that it's important for health and for avoiding injuries to have a few easy days on your workout schedule, where you exercise at lower intensity, and to take at least one day off per week.

If you have any risk factors for heart disease, such as a family history of heart disease, you might want to mention your exercise program to your doctor in case he or she wants to make recommendations.