I have just fixed why some apps work only with WiFi but not on 3G. ICS apparently automatically added Proxy-settings to your APN, in my case Vodafone (NL). This is not necesarry to even make use of mobile internet, and it also prevents some apps from accessing the internet. I removed the Proxy-settings et voila, it works perfectly again!
Fix: Settings -> Press 'Mobile Network' (not Off-On!) -> Names accespoints -> Click your provider -> Remove 'Proxy' and 'Port'
Apps not working on 3G:
- Soccer Live Scores (developer mailed me this solution)
- Rabo Bankieren (dutch app)
- OV Chipkaart Checker (dutch app)