Something that falls in a gray area (example for the user who asked for it in response to this same message): Running a node for your profile on a peer-to-peer social networking site which leaves all of your data on your machine in your home, under your own control. It has to listen for connections, it has to be up nearly all the time, it would use almost no bandwidth, but it would compete directly with Google+ and prevent Google from data-mining your social networking data.

Or how about a similar thing for email. Your email remains on a machine in your home, but you can access it from anywhere. Uptime should be pretty much always.

Or how about a commercial scenario? You realize your employer has huge overhead, and that you could undercut their price and offer your skills directly to customers over the Internet. So you start using your home Internet connection to do business. Not running a server, but violating the noncommercial usage policy. Running a business connection would just artificially replace your employer with Google and raise your overhead until it matched the employers, protecting the entrenched centralized business model (which the Internet should be destabilizing and destroying).

Give an example of something that falls in a grey area.

If I have to read fine print, then it is a grey area. If I have to interpret what they currently mean by "server", or what they may mean by "server" in the future, or what they may mean by "server" if I happen to piss them off for some reason, then it is certainly a grey area.

  Can I run a server from my home?

  Our Terms of Service prohibit running a server. However,
  use of applications such as multi-player gaming,
  video-conferencing, home security and others which may
  include server capabilities but are being used for legal
  and non-commercial purposes are acceptable and encouraged.

It is nice of them to be explicit with a few hand-picked cases, but that remains grey as fuck as far as I am concerned. What if I run a hairdressing business in my home and happen to blow through several terabytes in a weekend with git-annex? It seems clear to me that this should be acceptable, but I cannot feel confident it would become a problem.

Maybe it is clear to some lawyer somewhere, but it is not clear to me, the consumer.

  Our Terms of Service prohibit running a server. However,
  use of applications such as multi-player gaming,
  video-conferencing, home security and others which may
  include server capabilities but are being used for legal
  and non-commercial purposes are acceptable and   
  encouraged.

WTF? Our terms of use prohibit using a server, but some server uses, of which we will provide you with some examples but not definitions, are actually (contrary to what our TOS say) both allowed and actually encouraged.

So, thanks for telling us that your TOS doesn't actually mean what it says, but no thanks for not actually telling us what it does mean.

Yeah, my thoughts exactly. This TOS would comfort me if I were specifically interested in running a Minecraft server, but not much else.

If you're using the connection for a business in your home, then you are not using the connection for "non-commercial" uses and therefore should be paying for a Business Class of service

Who the hell defines that? What if I'm doing home accounting on my home computer and ssh into it? What if my accounting includes my spouses small hobby-business that is run from the home? What if I work a normal job but frequently VPN in and work from home? What if the traffic that makes them upset is not the traffic that is business related?

This shit is vague. It may be clear to you, but it isn't categorically.

Google does not offer a "business class" of service, so I can't pay for it.

Edit: OK I'm not really in a Google Fiber area, but I do pay for Comcast "business" internet for my house. I currently use about 5x more data than their residential cap allows, for 1.2x the price.