[[escafandra]]

#include <winsock2.h>


String GetCurrentIP()
{
   WSADATA Wsa;
   char name[255];
   AnsiString ip;
   PHOSTENT hostinfo;

   if(WSAStartup(MAKEWORD(2,2),&Wsa) == 0 ){
     if(gethostname ( name, sizeof(name)) == 0){
       if((hostinfo = gethostbyname(name)) != NULL){
         ip = inet_ntoa (*(in_addr *)*hostinfo->h_addr_list);
       }
     }
     WSACleanup( );
   }
   return ip;
}

Ejemplo de uso:

Label1->Caption = GetCurrentIP();

Saludos.