Kind of a complicated question in my household. My dad worked for the phone company so in late 95, early 96 (I believe) we had test DSL at our house before it was officially offered in our area. It was subject to random, unannounced and sometimes lengthy outages as equipment was tested, reconfigured, etc so dial-up remained on the computers at home as a backup. Then in about 97 or 98 the household went DSL full time, however because my dad was an employee dial-up was included in the DSL package indefinitely after that. It was almost never used but technically they still had it. I'm not sure when that finally went away.
The last time I can really remember using it was probably about 2000 during a DSL outage. I moved out in 2003 and the DSL I ordered for my place did not offer any dial-up access.
On a related note, looking through my records I see that the last computer I ordered that came with a modem was in 2006.