I have an original Kindle 3G and recently bought the Touch 3G. The reason I went for the 3G is not to download books but for two other reasons. Firstly for Whispersync so I can read on one device and then pickup on another at the same place, and secondly because the web browser will work abroad without additional charges. However, I have just discovered that on the Touch the only websites that can be accessed over 3G are Amazon and Wikipedia. This is a bit of a swizz as it was the thing that decided me to spend the extra on 3G. I know that Amazon would say that the browser is only "experimental" anyway.

Search Google on Wikipedia then click the link to 'Google Homepage', does that work?

From Amazon webpage about 3G touch:

WebKit-Based Browser
Kindle's experimental web browser is based on WebKit. It's easy to find the information you're looking for right from your Kindle Touch 3G. Kindle Touch 3G enables you to connect to the Kindle Store and access Wikipedia - over 3G or Wi-Fi. Experimental web browsing on other websites is only available over Wi-Fi.

Amazon are stopping use of their 3G for browsing going forward. It was reported some time ago. Because it was offered during the keyboard era they are maintaining the web browsing for kindle keyboard 3G. For now anyway, I expect that will go eventually too.

Not really a swizz, its been well known that the experimental browser on a Kindle touch 3G only works over wifi.

When you say "well known" I think that's a bit of an exaggeration, I consider myself well up on techie stuff and was not aware of it - anyway the device has only been out 3 weeks over here. No mention of it on the Amazon description.
Ironically I initially bought the non-3G version and the day I got it sent it back to swap for the 3G one specifically for the ability to browse abroad.
Perhaps not a swizz, but a disappointment.

No, it comes up with the message "wifi needed"

Yes there is, read the last sentance quoted by IvanIV above from the UK Amazon store