Universally renowned as one of the BEST Korean dramas ever, Coffee Prince is a must see. It falls under the "Cross Dressing" category, and there are many of them in Kdramaland. I, however, have only watched this one so I can't really make a separate category for it. It's one of the sweetest k dramas ever, with the powerhouse couple of Yoo Eun Hye and Gong Yu playing the main roles, and it's a great introduction to Korean dramas.
Coffee Prince is the story of a tomboy who, desperate for a job, applies to Coffee Prince, a cafe that only hires males. She must keep the charade up, even though she is falling for the owner. He's falling for her too, but he struggles with his feelings, as he thinks she is a boy. It handles the problems really well, and it just heartwarming and adorable. If you're going to start anywhere, this one is a good pick!