Typically I take maybe one rest day a week. Sometimes no rest day for 2 weeks. On a normal week I'll bike or swim in the morning, with up to 1 hour of running about 3 days per week in the evening.
I'm 38 years old, and I wonder if I'm overdoing it a bit. The only problem is that on my rest days I don't feel very good because I have not done much exercise, and I might as well forget about falling asleep that night !!
Back in the day when I trained a lot, I had the same problem. I found it best to use my off days as a fun day, like play basketball, golf, or someother game you may find fun but not to rigerous (key word is fun, and change it up week to week). As for training to much thats only possible if you are getting burned out, your developing an injury, or the obsession of exercise is destroying your life.
I think it depends on how fit you are. If you are just starting out, taking some days off completely are good for you. If you are really fit, for your rest days just do something that keeps you moving and is less that what you would do on a normal training day. On my taper weeks, I actually take real days off completely. It has worked for me. Just try different things out to see how your body and mind react.