To really give a good representation of the KPop Experience, it takes a little bit more than just a list of videos, "essential" or not. This list is intended to give anyone not familiar with the South Korean pop music scene a more well-rounded look some of the things that make it the modern entertainment phenomenon that it is.
Among people, especially westerners, who are interested in K-Pop, the question that almost always comes up in conversations, chat rooms, and forum discussions is: "Who will make it in America?" And that question is followed by a tossing out of various names followed by the reasons for each. You might say, "Well what about Psy? Gangnam Style?" Well, Psy (Park Jae-sang) is not really considered K-Pop by most aficionados. K-Pop has embraced him, naturally, since his overwhelming YouTube notoriety, but when "Gangnam Style" first appeared, Psy was a brilliant, Berklee Music School educated technopop auteur, a producer/writer/performer, who did not come from the mainstream of or represent the norms of what is considered K-Pop. And secondly, Psy was successful as a novelty act. Psy was shared by billions (literally) on YouTube because he was a crazy-looking, silly representation of what everyone expected from a Korean, or Asian in general. A great song, perhaps, but largely a caricature and not, to me, embraced for his star-power or musical vision. And as soon as his novelty wore out, he was forgotten, despite the release of several decent follow-ups.
My answer to the "Who will make it in America?" is simple. Nobody. And who cares? While the Big Three have all pushed a particular act in America at one time or another, SM's Girls' Generation, YG's 2NE1, JYP's Wonder Girls, they've all met with very limited success. The reason is simple and unfortunate, but it's not going away. Americans, who embrace other English-speaking performers and their accents with a slavishly mawkish obsession, they are repulsively xenophobic of any non-Europeans, and particularly Asians. That will not change. Americans expect their music to be in English, without realizing that the rest of the non-English speaking world has listed to their English artists for years. In fact, before there was K-Pop, most pop music in South Korea was, in fact, western. Michael Jackson, in particular, has had a huge influence in Korean pop music and that still bears out today. And that is always part of the reason that almost all K-Pop, almost by its DNA, includes English phrases. But that is not enough to generate a broad American fan base. I just don't see it happen. I believe that certain artists that have their own unique sound and approach and who embrace their Asianness (like Psy, caricature or not) have a chance to become a niche or cult favorite in America, but that is all.
And, the second part of my answer. "Who cares?" Why does the American market really matter? Of course, it does, but if you look at the inroads that South Korean music has made in other Asian countries, its doing pretty well without the Yankee Dollar. And continues to grow. It is simply remarkable that one country can export as much music as South Korea does. K-Pop artists have huge mainstream followings in gigantic markets: Japan, China, Thailand, Singapore, Malaysia, Vietnam, the Philippines, and more. Groups like Big Bang, Kara, T-Ara, and SNSD (Girls' Generation) regularly sell out in huge cities like Shanghai, Beijing, Tokyo, Bangkok, and now, due to the K-Pop cultists and the Asian diaspora in the U.S., they would sell out in New York and L.A., as well. And have.