I have recently encountered several users experiencing "No Wireless Internet Connections" after updating to Snow Leopard. Here are some steps you can take to try and resolve the issue. Most of the problems seem to be with wireless not wired connections.
1. You can go up to your Airport Bars in your Menu Bar and toggle the Airport On and Off.
2. If that doesn't work you can try restarting your Wireless Router as well as your Mac.
3. Finally if all else fails you can try this recipe which should lead to success
-Go into your router's administration page and find your DNS server(s).
-Open up your Network Preferences in your System Preferences window.
-Click on the Advanced section in the lower right hand corner, click on the DNS tab.
-Manually add the DNS servers you found in Step 1
-Save and apply the changes.
You should now be able to go online!
MACNERD Team