Learning Korean as a non-Asian foreigner is an exercise in masochism. Note that I specify "non-Asian". Why does that make a difference? Simply because Koreans possess a deeply-ingrained belief that non-Asians are incapable of speaking Korean. The self-fulfilling prophecy of it is that since Koreans expect you to be incapable of speaking Korean, due to this mental block, they are likely to not understand you regardless of your proficiency level. Additionally, they won't respond to you with normal Korean like they would respond to an Asian person, because they assume you couldn't possibly understand. You will rarely ever have an opportunity to hear natural Korean, because Koreans simply won't speak it with you unless 1) they are open-minded and awesome (meaning they have probably lived abroad - thank you to all of you), or 2) they have known you long enough that they've gotten past the odd sight of a foreigner speaking Korean.
In short, nearly every time you open your mouth and Korean comes out, you will be treated like a child or a circus monkey.
As a foreigner speaking Korean, you will begin every conversation the exact same way. Regardless of what you say, you will hear, "한국말 잘 하시네요!" - your Korean is very good. Every time I see a certain 할머니 in my building and say hello to her, she comments on how I "even know how to do greetings properly". That is, she is impressed with my ability to say hello. If you think this is a one-off thing, it's not. It is often difficult to move beyond this subject to what you actually want, because people are so caught up with the novelty of foreigners speaking Korean.
My Korean has gotten to the point where I sometimes think it would be better if I didn't know any. It throws people off that I can have difficult conversations. They simply don't know what to think about me, and in a society with such strongly defined thought patterns learned since birth, I think it miserably confuses people that I can converse in 우리말 ("our language"), because as a foreigner, I am not part of the 우리. I'm not part of the "we". Yet I understand the nuances between different verb endings, and I use the proper formalities when I speak.
Yet still, after conversing for awhile in Korean, I very often get asked if I can read and write Hangeul. The written language is literally the most well-structured phonetic alphabet in the world, taking less than a day to learn how to read, and people are amazed that a foreign mind could possibly comprehend it. This is a variant of "Wow, you're really good at chopsticks", and it's incredibly insulting. These micro-racial insults wear on you over time, and no matter how good you speak the language, you are never actually speaking the language - you are simply performing a trick.
I've gotten good enough at Korean that I'm offended when people use incorrect formality levels with me (i.e., when they talk "down" to me in situations where they would speak respectfully to a Korean). The first time I found myself offended, I was surprised at myself. But I realized that the language is not just a way of expressing ideas - it's a method of conveying culture and societal nuance. This was also around the time that I started "accidentally" using proper honorifics without thinking about it. Of course I still screw up from time to time, but I "get" it. Honorifics are more than simply habit. They convey a certain level of familiarity. In the same vein, I love when younger girls call me 오빠, because it means they've accepted me into a familiarity level normally reserved for Koreans. (On the flip side, when younger guys call me 형, it's almost always because they want me to buy something for them. I'm not dumb.)
So despite all this, despite all the pain and ridicule and incredulity and feigned misunderstanding, is it worth it to learn Korean? Absolutely, without a doubt, yes. Learning any language connects you with the culture in a way that nothing else can. Reading native literature allows you to peer into the collective mind of the culture that created it. Besides, what better way to give the finger to culturally-instituted racism than to be one of the few people that can understand the language swimming around the minds that comprise that culture?
Language is culture. Culture is language. There's no way around it. Koreans are protective of their language because they're protective of their culture, and given their history, it's not unreasonable to see why. However, you can't guard language, at least not very effectively, and the Korean language is a treasure that should be shared widely. Sharing is strength, because it stems from openness and vulnerability, while protectionism and racism are weakness stemming from fear. I look forward to a day when Koreans are eager to share their language and culture widely and without preconditions. Until that time, I'll keep reading my 만화, keep composing terrible Korean poems, keep singing my Korean karaoke, and I will undoubtedly give you a nice, big smile when you comment on my incredible ability to say hello. I am a monkey, after all.