Yes, most Koreans want North and South Korea to be unified under a single, democratic government. The people of North Korea suffer immensely under their government. The people of South Korea have to live with constant threats from the North. A unified Korea would bring peace and prosperity to all of these people.
The Korean people have been separated for over fifty years. Ever since the Korean War, and the subsequent Cold War politics, the Korean people have not been able to be the nation they want to be. It is true the governments and prevailing ideologies of both Koreas are substantially different, but this is not an impediment to unification, as shown by the examples of Germany and other countries example. The Koreans both want democracy deep down as well.