Honestly, I have a heart rate monitor (maybe two in fact) and I pretty much never use it. It's not that generally useful in my opinion.
Of course some elite athletes use them a lot, but as a non-elite athlete, I don't feel like there's a lot of benefit.
You can, for example, use a heart rate monitor to try to figure out what your max heart rate is for a given activity which can only really be determined empirically (The "225 minus your age" formulae were developed to keep recovering heart attack patients from getting into trouble and don't really mean all that much, not to mention that max heart rate varies with activity so, for example, max HR tends to be higher running than biking and higher biking than swimming).
You can then use max HR to estimate your lactate threshold without paying for a VO2max/lactate threshold lab test. In trained runners (say college athletes and above), lactate threshold usually is at 92% of max HR, but who knows where it is for guys like us? For us perceived exertion is probably pretty good lactate threshold training. If you're breathing hard, your legs have minor burn and you couldn't carry on a conversation, you're probably pretty much there.
Also all that stuff about "fat burning zone" they used to say back in the 1980s is mostly garbage. Not entirely garbage, but it does not take into account EPOC, which often accounts for most calories burned as a result of exercise. So though in theory it is the zone in which your body is burning fat *during* exercise, it's not the zone that burns the most fat as a result of exercise. The main reason to stay in the fat burning zone is because you will be exercising for more than 2-3 hours, at which point glycogen stores will be completely gone if you haven't been tapping into your fat reserves consistently. This, by the way, is why elite marathoners don't hit the famous 18-mile wall: they're going so fast they get there before glycogen stores are gone (among other reasons).
But do take your pulse in the morning for a full minute before you get out of bed. For me this is pretty a good indicator of health and fitness. Haven't done it in a while myself, but I know four things that drive up my waking pulse: lack of exercise, lack of sleep, abundance of stress and my wife waking up during and earthquake and jumping on top of me yelling. The contrary tends to drive it down.