Android service to check internet connectivity?

Services are designed for long backgroud running task. You should use a BroadcastReceiver:

This is a sample method I use to monitor the network state into my main Activity:

private void installListener() {

        if (broadcastReceiver == null) {

            broadcastReceiver = new BroadcastReceiver() {

                @Override
                public void onReceive(Context context, Intent intent) {

                    Bundle extras = intent.getExtras();

                    NetworkInfo info = (NetworkInfo) extras
                            .getParcelable("networkInfo");

                    State state = info.getState();
                    Log.d("InternalBroadcastReceiver", info.toString() + " "
                            + state.toString());

                    if (state == State.CONNECTED) {

                        onNetworkUp();

                    } else {

                        onNetworkDown();

                    }

                }
            };

            final IntentFilter intentFilter = new IntentFilter();
            intentFilter.addAction(ConnectivityManager.CONNECTIVITY_ACTION);
            registerReceiver(broadcastReceiver, intentFilter);
        }
    }

Remember to call unregisterReceiver when the onDestroy event occurs

Hope this help.