Extra workouts and Active Rest workouts
Here are some of my beliefs:
Days completely off help you recover but they tend to make you sluggish (lower level of nervous system readiness). This is especially noticeable when you have to perform complex lifts like the olympic lifts, maximal lifts and explosive movements. While one day of complete rest might not make a huge difference, I notice a drop in performance after two days completely off. This is not a loss of strength or power, just harder to get in the zone.
Active rest is better than passive (complete) rest to recover from workouts as long as the active rest sessions do not overstress the body. This can be due to enhanced blood flow to the muscles, activation of some biochemical pathways leading to an increase in protein synthesis and cytokines.
The more you do without exceeding your capacity to recover, the more you'll progress.
With that in mind I normally have 4 or 5 main workouts during the week. These are the sessions that are used to maximize the development of my main objective(s). For example, right now I'm focusing on the olympic lifts so I'm training them 5 days a week (4 on some weeks). If you are a bodybuilding it could mean doing 5 full on bodybuilding workouts, you get the idea.
I do not like to extend the workouts too much because I believe that after a certain period of time workouts become less productive: you lose some drive, your performance and focus decrease and your hormonal status becomes less conductive to maximal gains.
However my main workouts often leave somethings undertrained and some things need more frequent training (lower back and abs) and I do not include them in my main workouts.
What I do is include extra workouts and active rest workouts.
The extra workouts are short session, added to an already existing training day as a second workout. It normally lasts 20-30 minutes and is used to work on things like the lower back, abs, jumps and rotator cuff. These things are non-traumatic to the body and can be trained often. And they can never be too strong.
For example today I have an extra workout in which I'll be doing:
Jump 1/2 squat
4 x 10
4 x 10
4 x 10
I try to have 2 or 3 of these sessions per week. Sometimes they are shorter than that, never longer.
Active rest sessions are a bit longer workouts, 30-40 minutes and they are more complete. But you have more freedom. It's part of my plan... for example I can have 5 olympic lifting sessions then the 6th workout is a pressing workout.
In this session you can work on things that you feel were not hit properly in your main workouts or do stuff that you enjoy. Just stay away from really heavy work and excessive volume.