I will give my thoughts on each of them:

"The Eye" - Right off the bat, obfuscating the brand name like this is a bad idea. Look around on Logopedia [1] for a while and you'll notice that most corporate branding spells the company name out clearly. There's a reason for this. As beautiful as your stylized, geometric typography may look, it takes too long to get the point across. Human perception is variable; state your name loud and proud so all hear it. Further, yellow is a risky color in this case. It is traditionally used to evoke "sunny" feels but is more commonly associated with "caution" on the Internet. I also get this anxious feeling from the Eye of Mordor motif which reminds me of Internet surveillance more than it does freedom.

"The Connector" - I quite like the concept behind this one. One of the aspects of free software that I believe we take for granted is that open collaboration brings people together from all countries and cultures to solve common problems. I think the theme of "unity" is communicated effectively here with a fairly appealing minimalist design. My main criticism is in the geometry of the multicolored logo. The shapes are incongruent in their direction and give the larger logo a chaotic pull.

"Open button" - Once again, I like the concept of bringing people together. Unfortunately, this one just doesn't appeal to my tastes at all. The colors (which do not complement each other) and stroke come together in a very loud logo that not a lot of people are going to associate with "openness" (I'm not sure if that "open" icon is a standard or something the designer conceived of, but I don't recognize it). If I had to pick one word to describe this logo, it would be "garish". Tone it down and tighten it up.

"Protocol" - Nice touch with the `://`. As an alternate logo used in the context of API documentation, technical wikis, etc., I quite like it. However, I'll refer back to the obfuscation argument I made with "The Eye". You really want your corporate branding to convey that brand name as efficiently as possible. Again, eliminate any perceptual barriers to entry. This logo empathizes with English-speaking techies but doesn't necessarily translate well to other markets. If evangelizing free software is part of Mozilla's mission statement, they might find it beneficial to do so outside of the circles already using it. This logo falls short in that regard.

"Wireframe world" - Style without substance. Look at the IBM logo designed by Paul Rand [2]. It's strong and industrial while also having that little touch of personality that tells the story of IBM as a technology company - the scanlines. This visual cue is done so in a way that allows "IBM" to still be easily read at all distance. Compare that to this "Wireframe world" logo. The brand name isn't what is front-and-center here. Instead we get some lousy shape that tries to conveys an "M" and maybe a network? Either way, it's visually and conceptually unclear and not suitable for a corporate logo.

"The Impossible M" - This one's okay. Obviously M.C. Escher inspired, evokes the idea of technology that once seemed impossible. I enjoy what the designer is going for here. Compositionally it's very bold and works at a distance better than maybe any of the other logos. As far as my criticisms go, it looks a little stretched out. Maybe play with the proportions a bit. The colors look like they were rendered by a 1980s CGA graphics card. Try to go for a less saturated palette. I'm also not sold on the "MOZILLA" typography. The capitalization and kerning don't work well, although maybe it's the font itself.

"Flik Flak" - Refer to my comments about "Wireframe world". This is just more geometric trite that doesn't effectively communicate anything about Mozilla. The rotation and size of the type minimizes its role in the branding which is not good. Also not a fan of the colors here - your blue and orange sort of complement each other (would go for a more saturated orange) but the green completely throws it off.

[1] http://logos.wikia.com/wiki/Logopedia

[2] http://qz.com/461040/how-to-design-an-enduring-logo-lessons-...