I'm not sure about Europe, but I have found that it is very expensive to set something up with your provider here before heading out of the country (Mexico specifically in my case). Instead, you should be able to buy a card or dongle that plugs into your laptop (over USB or PCMCIA) and gives you 3G or better speeds. The trick will be finding options that don't require a contract.

Here is a list of options in the U.K.: http://www.top10-broadband.co.uk/mobile_broadband/

Is WiFi an option, or do you need to have the connection everywhere you go (assuming there is cell coverage)?

My own experience of using cell phone internet access from my UK service provider in mainland Europe was basically daylight robbery. I uploaded a few images, sent/received a couple of emails and ended up spending more than the monthly service charges locally and at home. I'd definitely recommend looking into local contract-free services before you arrive, but also consider that 3G coverage is spotty at best outside of the centre of major cities at least here in the UK and probably on the European mainland as well.

I've yet to find a reliable, affordable solution to get connected while travelling through Europe.

If you currently have a USB 3G modem from your wireless provider, take it with you and purchase a SIM card locally once you reach your destination. You may need to negotiate so that you don't need to sign a contract. Otherwise, roaming charges will be insane.

I travel all the time, much of it throughout Europe. I am based in the UK and I NEVER use my 3G mobile data connection, it will cost you a fortune. I only ever stay in hotels that provide wifi, it is possible and Europe is not that backward!!