I did a little more research and I am updating my answer with a more current solution. I am not sure if you have already looked at it but there is a nice sample code provided by Apple.
Download the sample code here
Include the Reachability.h and Reachability.m files in your project. Take a look at ReachabilityAppDelegate.m to see an example on how to determine host reachability, reachability by WiFi, by WWAN etc. For a very simply check of network reachability, you can do something like this
Reachability *networkReachability = [Reachability reachabilityForInternetConnection];
NetworkStatus networkStatus = [networkReachability currentReachabilityStatus];
if (networkStatus == NotReachable) {
NSLog(@"There IS NO internet connection");
} else {
NSLog(@"There IS internet connection");
}
@BenjaminPiette's: Don't forget to add SystemConfiguration.framework to your project.