I admit it, I'm a Type A person when it comes to riding. Nothing motivates me to ride like having a cycling goal and a structured training program to reach my goal. And yes, I love my heart rate monitor! I also love my cycle-computer, cadence, and altimeter! 
Nevertheless, I'm having a great time while I ride. I love the scenery, the challenge of getting up whatever hill it is I'm climbing, the funky conversations that come up with my riding partners, seeing someone else's confidence or ability improve on the bike.
Having the structure gets me out there so I can enjoy the ride. I'm the first to admit that the kind of structure I like would drive a lot of people crazy. But I do know that when I'm riding "just because it's fun," I tend to find other things that are fun and stay off the bike.
I guess the bottom line is that you need to figure out what works for you to keep cycling a fun hobby. Please, please, please don't read about the exploits of us Type A's and think that it's what you need to do to be a "real" cyclist.
I'll get back on the bike soon, I promise!