At least in most states, DSL service from the main telco can not only carry telco-provided ISP services, but also competitive ISPs, such as Sonic and Speakeasy and whatever Megapath and Covad are called these days. The competitors tend to cost a bit more, but also offer things like static IP addresses at more reasonable prices, and usually don't have usage caps or "no servers at home" policies. They may be renting just the wire from the telco, or maybe the wire and the DSLAM, and usually also some regional distribution network, but it's usually their own email and web servers and upstream bandwidth.
My experience with Sonic.net is that about every 5 years, something goes wrong that takes a day or two to fix, either a telco problem in a box down the street, or my DSL modem getting too old and dying. So I call them up by phone or send them email from work or Starbucks, and get a quick response back from somebody who can diagnose the problem but may need to call the telco to actually fix.
Fiber-based telco services don't have to share with competitors, unlike copper, and I'm not sure if AT&T U-Verse gets resold or not. But copper DSL is definitely not just the local monopoly.