For newcomers to Korea, some suggestions of extra things to bring.

Everyday Items

• Deodorant, especially if you have a specific brand. Deodorant is available locally, but can be expensive, and with a limited range.
• Large towels, especially if you're tall and prefer bigger bath towels or bath sheets. Daiso occasionally sells regular-sized, Western-style towels for 5,000 won, but this comes and goes. Bath sheets cannot be bought locally.
• Makeup (specific colors and high-end brands). Although Korea has a massive beauty industry, it is difficult to find foundation and base makeup that is darker than typical Korean skin tones. Korean eyeshadows also tend to be more muted, with less color payoff. Sephora ships orders of over 100,000 KRW to South Korea, but do not ship some brands internationally (for example, Kat Von D). You cannot use an American reshipper to get around this rule, because Sephora does not ship to business addresses.

Occasional Purchases

• Over-the-counter medication, in case you get sick before you can communicate effectively.  You also need to make sure that you don't accidentally bring something that you'd get in trouble for, without a prescription.
• Expensive electronics such as laptops, desktop computers, and tablets. Korean electronic products by Samsung, LG etc can be surprisingly cheaper outside of South Korea. You can try to buy online and have it sent in directly or by reshipper, but you will be heavily taxed for the total price (electronics+shipping) of 200 USD or more.
• Expensive items you may eventually want to buy online. Depending on what you buy, Customs will tax you for purchases of over 150 USD (general clearance) or 200 USD (list clearance). Buy it now, and bring it to Korea in your suitcase.

Maybe

• Tampons are widely available in South Korea, despite everywhere on the Internet claiming that it is a rare thing. You can easily buy them from Amazon.com and send them in via reshipper. For brands with various sizes such as Tampax Pearl, the only absorbencies/sizes available in Korea are Regular and Super. You will have to bring or reship Lite, Super Plus, or Ultra sizes.

Don't Bring

• Bedsheets and bedding. You don't know what size you'll need.  These are available in Korea, and while they can be expensive in department stores, they are really cheap on online stores such as Gmarket.
• DVDs and Blu-rays. Don't bother.