I'm currently based in SE Asia. Out here a number of dial-up ISP's offer pre-paid service, much like you'd buy time for a mobile phone. I'm not sure if Europe would be the same (I haven't been to Europe in about 6 years), but out here at least you can cheaply buy 10 hours, 50 hours, etc just by buying a card at a 7-11 or other corner store, punching in the scratched off settings, and dialing the number. Its pretty handy if you move around a lot within a small region (like SE Asia and Europe) and, more often than not, dirt cheap. It wouldn't be too much of a stretch to be able to find this type of service in Europe.
Truth be told, in places like Europe and SE Asia, the most popular way to get online is cell-phones. The people out here in Asia are cell-phone mad and GPRS is making a very big splash with at least 5 major telecom companies (from Australia, China, Malaysia, Singapore and Taiwan) coming together to create the largest and most advanced network on the planet. When I travel around in this region I rely more on my Sony Ericsson T68i for checking email and some web-browsing (although I had a chance to play with one of the 12" PowerBooks the other day, and it has left me reconsidering the way I do things. It is a very, very pretty machine.) The point is, out here, a cell-phone is almost always more useful than a laptop for checking email and doing some light web-browsing. Pre-Paid SIM cards cost next to nothing, and always come with access to WAP services. Everything I've read about Europe points to a very similar situation, particularly since Europe pretty much dominates the mobile phone industry (I once heard that there are something like 3 cell-phones per EU citizen.)
Still, what I said at top stands. You should be able to find some local ISP's that sell pre-paid dial-up time. And if you've got the technology installed, you should also be able to find a hotel lobby, cafe, or library with public Wi-Fi access. A quick Google search would probably turn up what you're after.
