Greens

I would say it depends on the person and their style of putting.  Some people will choose to play more break and hit it softer while others will play with less break and more speed.  The big thing is practice and figuring which style of putter you are and work on your green reading to see which way works best for you. 

I think it also depends on the kind of putt because with a short downhill putt with a lot of break it would be risky to hit it strong.

I agree with Nick P on this one. The only other thing I would add is that (for me) I will normally let the course decide how I putt. Some course have much faster greens than others. If this is the case I normally take a less aggressive approach and play the break and let the ball fall in the whole. Otherwise if the greens aren't concrete I am more aggressive.

PRACTICE AND EXPERIENCE.

KEEP PLAYING, EVERY DAY IS DIFFERENT.

I spend the majority of my warmup time feeling this out.  On a good course, where the greens are fast and roll true, you want to trust the break and let the ball find its way in the cup.  On less maintained courses, slow greens that don't roll true, I try to play more speed and less break.  

Also, I always ask the starter (if it's a new course for me, or I haven't played it in a while) if the practice greens are the same as the ones you'll find in play.  A little local knowledge goes a long way...

I concentrate 90% on the distance. Generally, the break is fairly obvious. I don't mean to sound flippant, or that I'm so good that I read greens like a pro because nothing could be farther from the truth.  The point is, if I handle the distance well, I'll usually not be off left or right by very much. On days when my distance judgement is off, I leave myself much longer putts long or short than I ever do by misreading the break.