By Boat: This list is certainly not exhaustive, nor particularly detailed, up to date, nor entirely accurate (help, anyone?).
To China: there are boats to Tianjin (the port nearest Beijing) and to a port near Qingdao (eight hours by rail from Beijing, so choose carefully) that leave from the ferry terminal in Incheon. The last subway stop on the Incheon line, I believe, gets you within a reasonably-priced taxi ride of the terminal.
I believe that both boats take about 24 hours, and I know for sure that there are two boats to Tianjin per week. The cheapest fare starts at about 110,000 won one way, and as I understand it, there are no reservations more than a few days in advance. There's a ticket office across the street from City Hall; otherwise you must buy tickets at the ferry terminal. Another neat aspect is that you can get your tourist visa on the boat, which certainly beats the chinese embassy in the Kyobo building.
There is also a 'slow boat to China' that leaves from Gunsan with destination for Shanghai, a whopping 48 hours-people I know that took it weren't particularly impressed. It costs somewhere over 150,000 won maybe in the 200,000 range one way.
I'd recommend the Tianjin one, though, having taken it about five times over the years. It's a good way to meet both Koreans and Chinese people in a relaxed atmosphere - and you get to watch a lot of smugglers hurriedly repack as the ship approaches port...
Last but not least, if you are interested in Russia, there's an excellent boat which takes off from Seocho and dumps you quite near the port of Vladivostok. The only problem being, that the port of Zarubino is still one bus ride and one ferry ride away from Vlad- leaving you a bit in the boonies, so to speak, and subject to all manner of Russian style traveller's extortions. Only for the rough and tumble travellers, but then again that's Russia in general for you. No on-boat visa service, not much in the way of amenities - if you just want a boat experience, go with the China-bound boats.