Of course I second the above.
I haven't watched it, but isn't Nodame Cantabile (both the original japanese and korean versions) exactly that? A quirky girl who follows a perfect guy around and he falls for her at the end?
With a darker tone, Que Sera Sera has that set-up as well: she's an oddball and he's a player who makes money by dating rich women. He gives her her first kiss, and although it's meaningless to him, he makes her fall in love with him. She then really, really sticks to him, but despite that he starts to grow fond of her - however his greed takes over and he turns to a rich woman instead, but becomes miserable as he realizes he's really in love with the weird poor girl. Won't tell you what decisions they make after that, but it's an interesting and unusual drama, however it's probably not to everybody's liking because it's not necessarily the most pleasant watch.
Myung Wol The Spy has a lighter tone than the previous, and kinda sorta has that situation, but a bit differently: she's a north-korean spy whose mission is to kidnap a hallyu superstar. Therefore, she does stick to him and follow him around and professes her love for him, but that's part of her mission (of course though she falls in love with him in the process). He falls for it and even though she's a nobody, he gradually falls in love with her as well. Several people disliked this drama though because 1) it had production problems because the main actress left in the middle of the drama, and although she came back it had an impact on the general tone of the drama 2) the guy in the beginning is a horrible jerk, but no worries, once he's in love, he makes a 180° turn and becomes the most lovesick character ;).
