Mobile internet pay as you go
Mobile internet without contract (aka pay-as-you-go, aka prepaid).
Suppose you're traveling to an European country for a week or so (e.g. for a conference) and you want to be self-sufficient in terms of accessing the internet from your laptop or mobile. So you don't want a contract, but you want a cheap pay-as-you-go rate.
Changing sim is not ideal, but roaming charges for data tend to be quite high.
In the UK, Virgin offers 30p/day for mobile internet on pay-as-you-go (very reasonably capped traffic). Essentially this is about GBP 10 per month for (practically) unlimited (mobile) internet, which is similar to what you'd get with a flat internet rate on a contract. (At low of pay-as-you-go deals used to be quite a lot more expensive.) The sim card costs about GBP 5.
In Germany, http://www.simyo.de/ offers a 30-day up-to-1GB pay-as-you-go for €9,90 (sim card purchase €4,90). Simyo cards need to be ordered over the internet - make sure you order it sufficiently well in advance!
In Spain, Simyo also offers a good deal http://www.simyo.es/ http://www.simyo.es/internet/, essentially €0,09 per MB, with costs limited at a maximum of €5 for up to 500MB. Simyo cards need to be ordered over the internet - make sure you order it sufficiently well in advance!
Time of writing: January 2009. Costs for mobile phone usage changes very rapidly, but you might find these notes useful.