Last winter I had a layover in Seoul, so I decided to take the USO tour of the DMZ. This is the only tour that takes you inside the Joint Security Area and you get to go into the negotiating room which sits on the North/South border (north side of the room is North Korea, south side is South Korea with a long table dividing it). A ROK guard stood at the north door inside the room to insure no one inside or outside attempted to open it. Outside the building was ROK guards and North Korean guards standing toe to toe on the border (a long concrete slab) staring at each other. So yes, I have stood in North Korean territory (technically).
We toured the Bridge of No Return, the Third Tunnel and the overlook that looks into the North (The Unification Observetory). An interesting note of the DMZ is it is a nature preserve now that is home to many wild species that live uninterrupted (thanks to over 1 million land mines) the Army soldier conducting the tour did say it's not uncommon to see 3 legged hogs running around.
Inside the JSA you definitely feel the tension as both sides are heavily armed. We had to sign waivers to go inside that basically said if war broke out they would try to protect us, but that's about it.