OK, we'll kick things off with the game that Kenneth first sent me, beginning this whole odyssey. If it had been less clever, maybe my whole trip through Kongregate would never have happened. Ah well.
(Brief disclaimer: As I discuss the game, there may be very minor spoilers. I certainly won't reveal how to solve puzzles, but I may discuss some mechanics which the game doesn't explicitly specify, though I'll try to keep to things which I think are pretty obvious. This is true in general, so consider yourself warned.)
So, the basic concept behind Chronotron, as mentioned above, is very, very clever. You're a robot with a time pod. You start out at some time (which, being a physicist, I'll call t0), leave the time pod, go around and do some stuff, and then return to the time pod. When you return to the time pod, you're transported back to the original time t0. Now, you see your past self go out and do all of the stuff you just did, but your current self can go off and do different things. Your two (or more) selves will never directly interact (that is, you can't collide with a past self), but they can indirectly affect each other in all sorts of ways, which is the heart of the game.
Most of the time, you want to keep the interactions relatively simple. A pretty common case is to go out, stand on a button which holds a door open for a while, and go back in. Then your next self will go through that door and do whatever you need to do on the opposite side. However, your future selves can also affect the past. Let's say that on the other side of that door, you accidentally trigger a switch that opens a pit between the button and the time pod. Now, when your past self tries to return to the time pod, he'll fall into the pit, which means he never returned to the time pod, which means you never created your second copy of yourself, which means you never triggered that switch and opened the pit, which means your past self could have returned to the time pod, which means...you've created a paradox! When this happens, you'll need to back up and try again. However, as the game helpfully tells you, "it's possible to alter the past without creating a paradox". This creates all sorts of interesting possibilities.
Now, some of the negatives. The most glaring is that the game is a little glitchy. Sometimes your past selves won't do what they did the first time around, even if nothing else has changed. This can range from slightly annoying to incredibly infuriating. The presentation is also a little basic. The background music is serviceable, but gets a little tiring after a while. The graphics are OK, while the sound -- well, the jump and pause noises are clearly borrowed from Super Mario Bros., so I doubt the rest is original, either.
A game like this is obviously going to depend heavily on its level design, and here the results are a mixed bag. The design is solid throughout -- there aren't any levels which feel like a real clunker, and there aren't any levels which depend on really annoying timing or positioning precision, which is definitely a huge plus. And each level (beyond the first few introductory levels, at least) will make you think at least a little (and some will make you think quite a lot). That said, there are a few criticisms to be made here, too. Remember above when I said that a common thing to do is to stand on a button to open a door for future selves to go through? You do this a lot. And going out, standing on a button for 20 seconds, and then going back is not really the most exciting thing in the world. It becomes even less exciting when you realize that 20 seconds isn't quite enough time for your future self to do all of the things he needs to do on the other side of that door, so you have to restart and then go out and stand on that button for 30 seconds instead. This gets boring pretty quickly. But also, remember above when I said that you can alter the past without causing a paradox? You don't do this very much at all. This has the potential to be a very interesting mechanic, but it's not really used very much in the game. There aren't many levels where you do something that seems aimless with your first copy, and then later copies do other things which turn that something aimless into something really useful, and this could be pretty fascinating (although in the wrong hands, I can also see how it could be pretty horrible).
Anyway, overall I gave this a 4/5, but obviously this concept has a lot of room to grow. I can see a sequel easily fixing a lot of these complaints and being a really excellent game.