Detect whether there is an Internet connection available on Android

The getActiveNetworkInfo() method of ConnectivityManager returns a NetworkInfo instance representing the first connected network interface it can find or null if none of the interfaces are connected. Checking if this method returns null should be enough to tell if an internet connection is available or not.

private boolean isNetworkAvailable() {
    ConnectivityManager connectivityManager 
          = (ConnectivityManager) getSystemService(Context.CONNECTIVITY_SERVICE);
    NetworkInfo activeNetworkInfo = connectivityManager != null ? connectivityManager.getActiveNetworkInfo() : null;
    return activeNetworkInfo != null && activeNetworkInfo.isConnected();
}

You will also need:

<uses-permission android:name="android.permission.ACCESS_NETWORK_STATE" />

in your android manifest.

Edit:

Note that having an active network interface doesn't guarantee that a particular networked service is available. Network issues, server downtime, low signal, captive portals, content filters and the like can all prevent your app from reaching a server. For instance you can't tell for sure if your app can reach Twitter until you receive a valid response from the Twitter service.

I check for both Wi-fi and Mobile internet as follows...

private boolean haveNetworkConnection() {
    boolean haveConnectedWifi = false;
    boolean haveConnectedMobile = false;

    ConnectivityManager cm = (ConnectivityManager) getSystemService(Context.CONNECTIVITY_SERVICE);
    NetworkInfo[] netInfo = cm.getAllNetworkInfo();
    for (NetworkInfo ni : netInfo) {
        if (ni.getTypeName().equalsIgnoreCase("WIFI"))
            if (ni.isConnected())
                haveConnectedWifi = true;
        if (ni.getTypeName().equalsIgnoreCase("MOBILE"))
            if (ni.isConnected())
                haveConnectedMobile = true;
    }
    return haveConnectedWifi || haveConnectedMobile;
}

Obviously, It could easily be modified to check for individual specific connection types, e.g., if your app needs the potentially higher speeds of Wi-fi to work correctly etc.