It is a good idea to bring more business type clothes. It is a formal country and most people will have suits or good Business Casual clothes. It is rare to see jeans and tennis shoes.
Toiletries and Medical Supplies: With so many people in hte city, bring vitamin C, multi-vitiamins, any cold medicine.
Luggage and bags:
A Big 24" luggage (preferably extendable and of light material) and a little carry-around bag for the to keep your important stuffs inside.
Clothing/Shoes/Weather Gear: (for autumn and start of winter... that's the time I went, so I'm not quite sure about the rest of the seasons)
Thermal wear, plain comfy clothes and a good down-feather or appropriate autumn/winter coat. (waterproof would be a better choice to shield you from the unpredictable rain) Nothing too heavy to pull your body weight down. It'll be good to add in a cap and scarves for those who are afraid of the cold. (Don't bring too many pieces, 2~3sets would be enough to last you through the cold weather)
Comfortable sneakers or plain canvas shoes would be the best with a layer of thick socks to protect you from the chilly wind. Don't wear heels and sandals/slippers are a no-no in Seoul.
Toiletries and Medical Supplies: Toothpaste and toothbrush are all you need.
And maybe little bottles of shampoo and shower foam in case the lodging's not providing you any.
Towels are optional. Some may not be used to using towels in the hotel but others don't mind it.
It's good if you contact your personal doctor prior to the trip or do a check-up. Bring airsickness pills, panadols and emergency medicine in case something happens. Although there are alot of "yak" stores (medicine stores) around, I never tried going into one.
Photo Equipment: For Dslr user:
Plug adapters, battery charger, extra battery to last for the day and more memory cards.
Probably 16gb memory space would be efficient to last you for a day or two if you are shooting jpeg format. (I brought my ipod, which served as a mass storage, and did photo transferring every two days to clear memory space from the cards).
For normal compact camera user:
Depends on how avid-shooter you are, I posted and shot everything I saw during the trip and 3 2gb cards were enough to last me throughout the trip.
Again, you need the charger for the camera and extra adapter for the plug.
Miscellaneous: A map and a guide book from the Korea Tourism Counter would be efficient to last you throughout the trip.
And, it'll be better if you would be able to memorize some key words and phrases.
Write down your accomodation addresses in korean for the limousine/cab drivers to know where you are heading to.
Clothing/Shoes/Weather Gear: i visited korea at the end of february/beginning of march. at that time snow was still covering the mountains and falling every now and then. it was still quite cold which is why i strongly suggest you bring thick sweaters/coats, mittens/gloves and caps/bonnets. thermal underwear are sure to keep you warm too!