I hate to one-up all of you (well, all right, that's not true, I actually love it), but I guarantee my problems here are worse than yours.
In the past year and a half, I have been forced to use dial-up for six months and, after that, had a faulty cable in the wall that cut the internet connection out for minutes at a time every few dozen minutes, making gaming impossible.
Also, my graphics card failed yesterday and it took me several hours to pin down that it was the issue before removing it and activating the integrated. That's not really internet-related, but it's limiting in a similar sort of way.
Anyway, depending on how severe whatever situation is, I usually have some backup plans. When I was on dial-up, I still had IRC and could transport things by flash drive, so I would download a single player game or something to my laptop and then take it back home and put it on my desktop. When the internet connection decided to start going out randomly, again, single player games were usually where I turned to. And now that I'm without a graphics card, I'm probably going to be sticking to older or less graphics-intensive games and maybe watching more regular entertainment (e.g., movies, TV shows, etc.), since all of those things can be done on integrated.
In the end, when you start having problems (and it will happen), the best thing to do (aside from fixing the problem, which is sometimes impossible) is find a way to adapt. Sitting there pulling your hair out isn't going to make it better, it's just going to drive you nuts.
As for how I solve connectivity issues, well first, I diagnose where the problem is. If I have no connectivity at all, I check all my hardware (wireless device, router, modem). If that doesn't fix it, I check the logs to make sure it's not anything on my end. If it looks like the problem's coming from outside, it's probably an issue with the provider and I call them up.
If I have any connectivity at all, I'll do a tracert and see where things are failing. Just Friday, my connection was really awful most of the night. I did a tracert to Google and found that the issue was two hops out from my location (packets started dropping there), so I was able to determine that the problem was at one of Comcast's local exchanges and that there was nothing I could do aside from call them and complain. So I played Civ4, which doesn't require internet.