I like this concept a lot.This sounds like a BT FON type service (where 'Foneros' or customers of this service can access other customers internet connections for a fee and then they get access to the connection.).I'd say look up the BT FON (or Fonero) service for more info.Hotspot owners can earn an income.I'd like to be part of this if successful so I can earn BTC for just renting out my internet to paying customers.I think a straightforward app/webpage (you can tell the router to divert people to on the 'guest' network mode where a webpage can be shown that says 'pay xxBTC for a days/weeks/months internet access or so)

My router is rather basic (Asus RT N10,I think) but has the ability to run 2 wi-fi hotspots at once (one for personal use and the 'guest' for the public to use)
If you can install a simple app that lets anyone rent out their internet connection,it'll be a success from the users point of view.When I get the summer off from work,I can contribute more to this concept. I want to make money from internet use.

That's kinda similar to the "pay TOR (exit) nodes with BTC" concept, there should be quite a few threads about this around.

Its definitely a similar concept.

I am taken with mesh networking but so far it hasnt taken off, I believe because there is no economic incentive. Adding bitcoin does this in spades. One might also add  piratebox http://wiki.daviddarts.com/PirateBox for local secure file sharing and provide the same economic incentives. Think sneakernet on steroids.

1)  This likely violates the ToS of any residential internet service.
1b)  People could browse naughty areas of the internet, and YOU would be the one to get in trouble for it.
2)  It's largely pointless considering the small number of people who use Bitcoins.  Like P4man said, the likelihood of someone who uses Bitcoins is walking in your neighborhood looking for internet access is incredibly slim.  Of course, if Bitcoin got big, then I could see it as a viable option, as long as 1) and 1b) can be worked out.
3)  I like the idea of simply changing your SSID to show "Bitcoins" or "UseBitcoins" or "ISupportBitcoins" or something else to that effect.  Kind of free advertising for Bitcoin.

I believe it can be done in a way that it's not very likely that you'll get caught. Especially if the bandwidth usage from that is not massive. I have a 100mbps connection which is fairly common here and no one would care if I share 10mbps. There are no quotas or limits either. Using some kind of encryption/VPN should be explored also for increased security.

Finnish ISP's commonly use what is called DNS filtering to block these sites. Other than that, the same concerns go for point 1) which can be countered by features that encrypt the traffic.

This point is just stupid. The concept we're talking here is revolutionary, it's the kind of thing that would attract people to learn about Bitcoin even if they don't know anything about it in advance. In Europe it's a very common problem that when you travel to another European country, using your local 3G is super expensive and buying a 3G package from there is a pain in the ass. There is no wlan available everywhere either and if there is, it's often not free and requires credit card information. This has the potential to change everything.

This is something that I don't think has any effect because most people don't even know what Bitcoin is, telling people that "I like Bitcoin" in this way means nothing and it's not going to lead to people finding out. Renting your connection with bitcoins however is something that could spread like wild fire and start getting attention. An open wlan with a login page having bitcoin payment instructions would in itself be huge.

Of course it is smart to think about how ISP's would respond to this, that's why I mentioned exploring VPN possibilities.

You could even offer WebGL/JavaScript miners - once a share is mined, they get access to the network and can submit a transaction for more funds on their account for bandwidth or just keep mining, if they have fast hardware.

This has been talked about before.. I also think this would be amazing to do with bitcoin..

But more than half the work is done for you..

dd-wrt, with Chilispot, or Freeradius is the programs your looking for..  Charge a small fee for access to your internet over wifi. 

So far I see bitcoin being far superior to paypal for these purposes..

In case anyone would like to read a recent discussion on the topic:
[IDEA] plugin for dd-wrt that allows selling internet connection to neighbors

I'd like to reiterate the suggestion for "offline" transactions like with the BCCAPI, that would be pretty cool.