I know that Rakuten is Japan's most popular shopping service.Companies that cater to their foreign customers (i.e. Bodyline and Chocomint) will usually have a foreign shipping option through Rakuten on their website. However, I've heard that small independent shopping services are the way to go.
I personally use a small indie shopping service, myself. I use Chibi Tenshi's service on Livejournal.
I also hear that Mochi Machine's shopping service is great! They seem to be the most popular.
All you have to do is send them a link to the item you want and they will order it for you. You will have to pay extra for the services (usually 10-20% of the total cost), plus shipping and handling. They all use Paypal. They both also do in-shop services. So, if there is something you really want, not sold on the company's website, they may go into the store and get it for you. However, they only do this for some stores, so make sure to ask where they do in-store shopping!
I haven't bought anything from South Korea yet (or North Korea, but I think you could have guessed that). Now, I have spent some time looking up Korean shopping services and these seem the best from what I have seen. However, I haven't used them before, so don't take my word for it!
I hear that Sunkyung on LiveJournal is doing a shopping service. You might want to ask about it.
Watertonkorea has some recommendations. I don't know how they are, though.
I also seen a few people recommend Koreanshopping, however I've seen some pretty bad reviews on their site, so I would be careful...
Minarin shop does orders with or without Paypal. They say they
"do not do any other Koren stores, but you can submit a request."
Sechuna-pers does group orders.
Last, but definitely not least is Gmarket. Gmarket is basically the same thing as Rakuten, but in South Korea, instead of Japan. Just like Rakuten, you can buy items straight off of their website. They have a very extensive selection. The only downside is that you can only purchase what they offer. You can't requst them to order something for you that they do not feature on their website.
A great place to buy items from all over East Asia is AsiaJam.
Don't forget to look them up.
I hope this helps! Thank you for looking!