Wherever I've worked internet access has been a major reason for unproductivity
You mean something like your 1223 posts?

I note this last one is business hours, too. At least I have an excuse, it's my business
OK, seriously though, although it's very healthy to sit and think "what could go wrong" with important infrastructure, predicting likely gloom and doom is another thing - I honestly don't see any major threat, save perhaps gross lack of investment in supply. Terrorists? Puh-lease, somehow I can't see Osama sitting in the desert with his satellite uplink coding up the next great Windows worm *ooh ... terror struck into heart*, I'm not sure that even falls under the definition of terrorism. Terrorists want to, um, "terrorise" you - making your Internet go down must be pretty low on the list of "scary things to do", just underneath "stand behind a corner and jump out and yell 'boo' when people walk past".
I think the most likely scenario, given how lousy Windows security is, is a really bad maliciously coded worm. Even a worst-case worm though, the damage will be highly limited - very little "basic infrastructure" equipment runs Windows (routers and major servers), it's mostly an incredibly heterogenous mix of UNIX, Linux and various other proprietary, custom systems, while even desktops are highly heterogenous these days (except Windows, but even there). Also, the damage will be quickly limited - AV companies will produce patches, most infected boxes will be taken offline, most companies would be protected by firewalls, many home users by their NAT routers, and ISPs could even cut certain customers off if it became a big problem. Most worms are coded with financial motive though, i.e. Windows botnets, and zombies are useless to spammers if they clog up the Internet entirely. Bad worms would also be self-limiting, taking out the very infrastructure they need to spread.
I can't help but think, especially when the word "terrorism" is thrown in, that these kinds of 'scaremonger' groups are just looking for funding, spouting alarmism so that government etc. throws some money their way, so they have jobs again for another year, sitting around talking nonsense. Must be budget allocation times coming up again.
Anyway, thanks to Telkom, my business already expects the Internet to quite possibly go down for days or weeks at a time
The Internet was originally specifically designed and built to be able to continue even if large portions of it were taken out. Reliability is in its very design, even if its not perfect at that.