holy crap is this the topic for me! I am not watching one currently but I have made my way though most of them on DramaFever! I prefer the romantic comedy ones the most.
I think the best one is "My Girlfriend is a Gumiho", but I have serious soft spots in my heart for "Boys Over Flowers" (of COURSE), and "Stars Falling from the Sky" (soooo wacko!). If you have not watched "Soulmate", I would recommend that, it's a kind of cool one that's more adult, but isn't as popular.
I could keep going!