Earlier quoted context omitted.
This is against the ToS for most residential internet providers and can subject you to disconnection/ban from one of the few/only carriers available in your city.
How tyrannical. In Romania, my ISP Digi gives me a free domain name.
Business plans typically provide either an SLA or at least less likely to employ traffic shaping. Residential plans tend to thus prohibit running a public facing server for commercial purposes, since they're over-provisioned on the assumption that residences don't always fully utilize their capacity. This is becoming less of an issue with fiber optic internet lines, but coaxial cable networks can easily see a few heavy users adversely impact everyone else.
All of that said, I've never lived anywhere with an ISP that prohibited public facing home servers- they really only had the stipulation about commercial purposes. I imagine if your server was receiving a ton of traffic (say, a popular blog) you'd get a nasty letter about it, but I don't know of anyone who has run into it.