What to do if your iPhone cannot surf on Wifi

I just had a bizarre issue with my iPhone - It was on Wifi at home, but could not access anything on the internet.
When opening the built-in apps from Apple like Safari, I got the following error:


I tried restarting it, and even Reset Network Settings in the Settings section. Still didn't fix it. Note that using the laptop and mac mini on the same wifi network was fine going online.
The one thing that I did find useful was to set the Wifi settings from DHCP to Static, and removing the DNS entry there and replacing it with the OpenDNS servers. Type in these IP addresses then try again:
208.67.222.222, 208.67.220.220

EDIT: Seems that the laptop and mac mini already had the OpenDNS entries placed into their network settings... explains then why those worked fine!