All suggestions are welcome, please add them into this thread!
I concur, great work team and very much appreciated… and I can’t resist a suggestion too 
It is a global network without servers that offers a level of security and privacy not currently available on the existing Internet.
I wonder about changing available to possible?
I accept this is only the brand description and that I may be being too detailed, so just offering the idea!
Thanks again. I’m really enjoying this process and watching it all unfold.
I’ll put this here on the back of that brand is reasons why you would want product:
I wonder there is an opportunity for SAFE to leverage those principal aims that are Privacy; Security; and Freedom, in an explicit way that I’ve not seen suggested yet.
“SAFE because”
SAFE because - you should not have to ask for privacy
SAFE because - everyone deserves freedom
SAFE because - security should be without compromise
or similar.
I don’t know if that is beyond strapline and more into the area of meme and perhaps with branding that matches the intent and direct statement that is what SAFE is all about.
Branding should be compelling… not just another option that you might want, but something that is essential to providing what you need.
I wonder we should not be shy of being explicit in defence of those fundamentals that should appeal to all sensible interests. Should of course is opinion but that then strongly founded in understanding ‘why’ such capability matters. As such, the hook there might be considered contentious but it draws people in… and marketing is all about hooks.
The branding should make the product appear essential and needed, not just another product that user has to come to with a reason to use it. If we provide the reason up front, then the user has even less to do in falling towards using it.
SAFEnet’s true peer-to-peer authentication appears to be unique, and so any service that requires a login can be serverless only on SAFEnet.
We applied some of the changes suggested by @Pierce. Here is the final version that we agreed on:
The SAFE (Secure Access For Everyone) Network is a decentralised data and communications network made possible by efficiently combining the unused hard drive space, CPU power and Internet connections of its users. It’s a global network without servers that offers a level of security and privacy not currently available on the existing Internet. Users of the SAFE Network have full control over their data, while software developers can focus their time building on top of a secure infrastructure.
The logo competition is now live. See this topic for more info.
Two minor adjustments if you’d allow. Sorry if I’ve become a nuisance. 
First.
There is a tiny redundancy in this opening sentence. It’s technically correct but as you guys know, I would link anything SAFE to be smooth, shiny, and succinct. 
My adjustment would be:
SAFE (Secure Access For Everyone) is a decentralized data and communications network made possible by efficiently combining the unused hard drive space…
OR if you’d still want to use a forced reference by using the word The, we could try this:
The SAFE (Secure Access For Everyone) Network is a decentralized data and communications platform…
Second.
The two its/it’s are too close together. I believe it would roll off the tongue more smoothly if the second were not contracted.
The minor change would be:
CPU power and Internet connections of its users. It is a global network without servers…
That’s all, sorry to pester you. 
One other minor change that someone once said to me. When you refer to the Internet rather than a interconnected network that one should capitalise “Internet”.
The Secure Access For Everyone Network , SAFE , is a completely decentralised and serverless protocol efficiently and securely combining various unused resources of its users . Hard drive space , CPU power and internet connections are streamlined into a global and decentralised data , communication and application environment offering unprecedented levels of privacy and security currently not available on the existing Internet ( SAFE Users call it the Clearnet ) .
All participants in the SAFE Network retain full control of their data and credentials , its users can choose to surf or create websites , store private and public data , make their unused resources available and gain safecoin currency in exchange for running local vaults , trading services , and even by executing native dapps or selling their own computing power .
Software developers appreciate the advantages of being able to focus their time and
energies building and pioneering on top of a secure and innovative infrastructure
through is SAFE protocol the creation of an improved and new internet experience .
As many voices say , it may well be The Internet 3.0 Innovation so many of us have
been impatiently longing for . Now , the waiting is over , rejoice with us and join the
best internet network now . Explore , create , and prosper freely in all ways possible !
Feel free to use , change or dismiss any part of it …
Thanks everyone for the suggested improvements. 
We’ll surely discuss these the next time we meet. For the logo competition we have already used the version posted in my previous message. We won’t be changing the text we used for the 99designs competitions, but I’m sure there will be other use cases in the future.
With a capital P “P”).