No, there won't be war. These kinds of incidents happen about two or three times a decade. I lived in Korea for half a decade and when I was there a South Korean farmer caught NK commandos still trying to dig under the DMZ (anybody remember the 80's arcade game Dig Dug? Same thing, I swear) and some NK and SK gunboats both opened up on each other with their mounted machineguns. A friend of mine was doing his military service at the time and told me how his boat, that arrived on the scene later, was fishing bodies out of the sea.
Every now and then North Korea has a spaz, South Korea throws some rice and a couple of diesel trucks at them, and everything returns to normal.
One thing though, this is the first time to my memory that a multimillion dollar vessel was actually sunk. I think that's given quite a few consumer-driven, apathetic Seoul residents cause for pause.
I would have to agree with junglecrawler. NK rattles the saber and sometimes gives a paper cut wound to SK but never much more. I highly doubt SK would ever do anything more then turn the other cheek. For SK to declare war, NK would have to do it first and NK wouldn't want to take that politcal risk (the old who hit who first is the person at fault). To many people still remember the Korean war over there and know that if SHTF for real.... well millions would die in a very short order. Actual war over there would be NK rolling across the DMZ.
Right now, though, both sides are on high alert, and that's when stupid stuff happens.
When I was there we had constant alerts because of tree trimming incidents, guys accidentally driving over the DMZ line, you name it. Tunnels were a constant thing, to the point they did not create alert status changes anymore.
Gotta say, I never heard of the North sinking a ship before. They have fired rounds back and forth from time to time, but a sinking has to have a lot of folks scrambling and doing alert related tasks.