Ok, the photos help... from my observations and personal experience, when you need to make a bar chord, you're going to need to slide your thumb in behind the fretboard like you are doing for the first few photos. When your doing open chords or soloing, you may want to adopt a position more like what you are doing in the last photo, where you allow your thumb to wrap around.

Again, I don't want to set off any fireworks here, so please understand that there are players, particularly guys that "shred", playing very fast, that will definitely keep their thumb behind the fretboard in the more traditional position. However, these guys often have a very different sound & style that allows them to BARELY put any pressure on the string to make it sound properly... we're talking flat, "fast" necks, light gauge guitar strings and super-overdriven tone. If you're looking at more traditional rock players like I mentioned before, you'll notice that when soloing they tend to allow their thumbs to wrap around, especially when bending, as it really adds support, but also I think its just an over-all more comfortable position.

With a little practice, you should be able to easily fret open chords with the wrapped thumb position that allows your wrist to be straighter than with your thumb directly behind the fretboard. Here's pics I took with my i-Phone to show you what I mean:

This is the traditional "thumb behind the fretboard" position. I find this makes my wrist pretty sore easily (notice how I have to bend my wrist around to get my fingers into position):


Hope this helps. Really do watch for well known rockers to be using the "thumb wrap" technique... you'd be amazed how many guys play like that, so I think there is really something to it.