It was sometime in late 2003 (December-ish) I last used a dial-up modem.
I initially ditched dial-up for ADSL in early 2001 (512k/384k), but in fall 2003 a faster ADSL option (8M/1M) was offered in my area and I signed up for it. And I also cancelled the old service at the same time. (During this time there wasn't a smooth way to switch DSL providers in Sweden. It was shortly thereafter that they worked out a consumer-friendly way of doing it). But there were significant delays in getting the new DSL service as it was pretty popular.
So I had to go back to dial-up for almost three months. I found a provider that offered a semi-flatrate (X minutes for Y money, thereafter Z money per minute [I don't remember the exact rates]). It got kind of expensive for my student budget. A $100-150+ USD equivalent extra cost per month was not insignificant. But in the end I got my faster ADSL connection and I was happy.