Superfriendly,
I travel a lot with work, and spend quite a lot of time in Europe.
The cheapest way I have found is to use GPRS on a Vodafone connection. They don't charge you for being abroad, just for the amount of data you pull or push through the network.
The Vodafone ISP is free anyhow to Vodafone customers, and my true ISP is Pipex Dial. I have no problems downloading my Email or if neccessary downloading files off the internet.
Depends on how much you want to use it as to which is the cheapest option.
A Standard Pipex account is £ 14.99 per month + £ 5.00 for the global roaming service (only charged when you use it). There are local dial ups in every country I've ever been to. The reason I use GPRS is I find the hotel rip you off going through their switchboard even if the local call is cheap.
Vodafone charge £ 15.00 per 5Mb of data. Sounds like a lot, but if your just using it for Email, you should find that you don't get close. Web sites too are fairly low on the data front, unless thy're very graphics intensive.
I'm not sure but I believe most of the mobile phone providers now have GPRS up and running on their networks.
Hope this helps,
FWyg