JW, I feel that III should have gone before II; III teaches you to push laterally, and II teaches you that you can't pull (which is a step more complicated an idea, I feel). Your last one is pretty fiendish.

NiallM, I like how some of your levels have clearly defined 'loops'. Makes those levels feel a bit like one's going on tracks.
HybridMind, the quality I like about your levels is that many of them are not straight-forward, they do require you to do things in a backwards way. Most could use some trimming, though.
Draknek, I feel that your levels are not very well ordered. Some early ones offer interesting challenges, while some later ones seem fairly trivial. The last one's really smart!
Some general criticism:
As JW has said, it's typical to waste space in one's levels. For small puzzles like those, less is more, so it's 'good' to reduce everything to make it as tight as possible. What this results in is increased clarity: you've reduced the possibility space to only that which is interesting to the resolution of the puzzle--you've cut the chaff. Particularly, in very large levels that have you repeating the same action and going back and forth, it's added tedium; the player already solved the level in their head, but they have to go through the motions just to get the game's approval (this, sadly, happens all the time in mainstream video games that tend to be measured by 'hours of gameplay').
I guess that what stems from this idea is that, if you want it to feel fair, make your level understandable. Cut out all the intricacies that make the ideas behind it less clear.
But of course, you can learn double by taking a certain pattern and reversing it. If, instead, you want to create a level that is seemingly very complicated but in reality has a very simple solution, you can increase the possibility space by intentionally adding the intricacies, thus causing confusion. You can make the player feel like they're working by making them do repeated chores devoid of mental challenge. You can make a level seem more natural by leaving the door open to alternate solutions and experimentation, no a set single solution.
edit:
Lord Tim, I liked your 'thinking out of the box' series, though the ideas are repeated a bit. Level 9 reminds me of a game of go.

Some of your levels feel very natural, in the sense said above.