I wanted to take my entire trans-Asian trip without flying. Obviously, the first challenge would be taking the ferry from Japan to somewhere. Nearby Korea was the obvious choice, although there are also occasional ferries to Shanghai and a port near Beijing.
I had read that you could get a combination train and ferry ticket between Japan and Korea, and that these tickets were sold at a significant discount. It was fairly difficult to get information on these, even at the normally reliable seat61.com, but I discovered they were called nikkan kyodo kippu (日韓共同きっぷ).
These tickets allow for Shinkansen travel from most cities in Japan to the ferry port, ferry travel between the countries (you can take either the fast and expensive Beetle ferry from Fukuoka, or the slow overnight ferry from Shimonoseki at the western end of Honshu), and then the fast KTX train from Busan to Seoul. Obviously, I am cheap so I took the overnight ferry, which has the added advantage of saving one night's accommodation. I've heard that the fast ferry is noisy, bumpy, and that you aren't able to really walk around or go outside during the three-hour trip (similar to the much shorter Hong Kong-Macau jet-foil), in which case the slow ferry is an even more obvious choice.
I eventually found pricing information on a blog by Louise Rouse—her blog is now defunct, but you can still access an informational PDF she translated here (I've screen-capped it in low-res below, in case her link ever goes dead, but you can click through to her PDF). The only thing that remained was to actually buy the ticket. I discovered that you really can't buy them at your average JR ticket counter, as they have no idea what these tickets are (even if you speak Japanese, as my Japanese friend discovered). In order to buy these tickets, you absolutely do have to visit a travel agency. Thankfully, every train station of any size will have a travel agency either inside the building or across the street. I bought mine at the TiS agency in the Hiroshima train station, and after dealing with JR ticket staff I was actually kind of surprised that the agent immediately knew what I was talking about and was happy to make me a ticket (and spoke pretty good English, too). When you buy your ticket, check with the agent whether you will also have to pay the fuel surcharge when you check in (you will definitely have to pay the port fee, and they will only accept cash at the check-in desk).
You are allowed to take up to seven days to complete your trip from the time you begin, and on my ticket I had to specify the shinkansen and ferry dates in advance (the date of the Busan-Seoul leg was left open, and had to be confirmed/exchanged for a proper ticket at the train station Busan, which I did for a train that left 30 minutes later). You do not have to specify a shinkansen time at the point of purchase, and you can simply show up at the shinkansen station any time on the designated day and take any non-Nozomi train, sitting in an unreserved car (the first five cars are typically unreserved).
If you are traveling from Korea to Japan, it may be easier to buy one of these tickets: I saw it advertised at the KORAIL ticket office in Busan, and you can see Korean pricing here.
You can see my blog post about the ferry from Shimonoseki to Busan here.