1.

WifiManager wifiManager = (WifiManager) getSystemService(WIFI_SERVICE);
WifiInfo wifiInfo = wifiManager.getConnectionInfo();
int ipAddress = wifiInfo.getIpAddress();

2.

try {
    Socket socket = new Socket("www.droidnova.com", 80);
    Log.i("", socket.getLocalAddress().toString());
} catch (Exception e) {
    Log.i("", e.getMessage());
}
public String getLocalIpAddress() {
    try {
        for (Enumeration<NetworkInterface> en = NetworkInterface.getNetworkInterfaces(); en.hasMoreElements();) {
            NetworkInterface intf = en.nextElement();
            for (Enumeration<InetAddress> enumIpAddr = intf.getInetAddresses(); enumIpAddr.hasMoreElements();) {
                InetAddress inetAddress = enumIpAddr.nextElement();
                if (!inetAddress.isLoopbackAddress()) {
                    return inetAddress.getHostAddress().toString();
                }
            }
        }
    } catch (SocketException ex) {
        Log.e(LOG_TAG, ex.toString());
    }
    return null;
}

3.

WifiManager wifiManager =  
 (WifiManager)getSystemService(WIFI_SERVICE);
DhcpInfo dhcpInfo = wifiManager.getDhcpInfo();
 
String[] dhcpInfos = dhcpInfo.toString().split(" ");
String realIP = "oops, no ip";
int i = 0;
while (i < dhcpInfos.length) {
  if (dhcpInfos[i].equals("ipaddr")) {
    realIP = dhcpInfos[i+1];
    break;
  }
  i++;
}

4.

WifiManager wifiManager = (WifiManager) getSystemService(WIFI_SERVICE);    
    WifiInfo wifiInfo = wifiManager.getConnectionInfo();
    DhcpInfo dhcpInfo = wifiManager.getDhcpInfo(); 
 
// [...]
 
tv = (TextView) findViewById(R.id.id_wlan_ip_address);
tv.setText(intToIp(dhcpInfo.ipAddress));
 
// [...]
 
    /**
     * http://teneo.wordpress.com/2008/12/23/java-ip-address-to-integer-and-back/
     */
    private String intToIp(int i) {
    return ( i        & 0xFF) + "." +
    ((i >>  8 ) & 0xFF) + "." +
    ((i >> 16 ) & 0xFF) + "." +
        ((i >> 24 ) & 0xFF)
        ;
    }