I do not use a heart-rate monitor. If you know or even understand some basics about human physiology and how it adapts to training you can get what you need with a well thought out work-out program. However I do think it's important to check your resting heart rate once in awhile to see that it's getting lower and lower. If you are truly getting fitter, it should be.
you want to be working your v02 max, anaerobic capacity/threshold, cardio-vascular conditioning. I don't know where my heart-rate is when I do sprint intervals for example (it would cut into valuable time where I could be walking or running, concentrating on recovery before the next interval) but hell, if i'm about to puke, if my vision starts going shaky(draining of color) if it feels like i'm about to give out and push through it, trust me your heart-rate is where it needs to be.
My resting heart rate is now 52, down from around 60 from about a year ago. I hope to get it down to 49 at least. (trekking through hellish snow for miles seems great for this).
Also looking into other professional athletes. I thought for awhile that sprinting was the best way to increase v02 max, then I found out some professional "hikers" who hike for miles and miles with heavy loads seem to have incredible vo2 max, very low resting heart rates, incorporated that on some days when I wasn't sprinting.
I think there's a lot better ways then monitoring your heart rate. When training for running I have to do all I can to push through the pain, the nausea, sometimes to not black out. That takes all the concentration I have.
When you really get going it's all you can hear, your heart pounding in your head. Now if you have heart-problems or etc, sure good idea. You should be able to get a natural "feel" for where your heart-rate is after awhile. If your in the "proper" zone.
Hell one even came with a set of nordic "walking sticks" I bought. never touched it. Another insane workout that translates into better running. Running with the nordic sticks with weight, uphill again and again.
Or for example in weight-lifting. I know I have a good heart-rate going after a set of 30squats because i'm drenched in sweat, pouring sweat like I've been sprinting intervals, my vision is kind of "fading back in", I can hear my heart beating in my head, I know my heart-rate is where it "needs" to be.
I concentrate more on the time of the run or bike-ride, that you are progressively getting better on a "timed" loop or some-thing. Though a lot of runners say even that is questionable, that you should train against "yourself"
I'd say keep a log, make sure you keep records of your exact time. An ironman triathlon watch will give you a 50lap memory, some interval timers, a stop-watch, all that you really need. When you look over a 1mile or 6mile(or longer for a bike) "loop" or "track" and how well you've run or biked or etc it over the last 50 times, and keep logs of nutrition, training schedules, etc you can get a really good idea of what's going on and what helps, what doesn't.
I don't train for marathons though, just to run the mile as fast as I can, to be a powerful sprinter, and a good 6-10mile runner. A marathon would probably kill me.