Korean food is notoriously hard to pair with wine. Since there are so many intense flavors and aggressive scents in your average Korean meal, it's not as straightforward as pairing wine with a Western meal.
The trick is to make your wine decision based on the main dishes of the meal rather than the banchan (side dishes), since the latter will almost always include spicy, sweet, or salty flavors. And although there are usually at least a few spicy elements in a Korean dinner, these flavors are usually complimented by the other soup, rice, or noodle dishes in the meal. So don't just focus on the high spice factor unless the highlight of the meal is something like spicy grilled pork or a hearty kimchichigae , a spicy stew made of kimchi, pork, vegetables, and tofu.
For Korean meals with spicy main dishes or when the main element is a spicy stew:
A dry, light Riesling or a crisp Sauvignon Blanc are my personal choices for Korean meals that are heavier on the spice than usual. Nothing too sweet, fruity, or complex. Avoid heavy red wines.
For a Korean barbecue dinner:
Bulgogi and Galbi are smoky, sweet, and full of flavor, so a bright and simple red wine is your best bet. An Australian or Chilean Shiraz are my personal favorites but Chianti or an American Zinfandel are also good choices. Again, you want to avoid anything too complex, heavy, or earthy that will compete with the explosion of flavors in a Korean bbq dinner.
For a Korean dinner which features seafood:
Koreans love fish, shellfish, seaweed, and everything else in the sea. If you will be eating broiled fish or a lot of seafood in the meal, try a chilled rosé or a dry white wine like a Pouilly-Fumé. A general rule of thumb for pairing wine with Korean food is to avoid anything too bold or tannic.