For me it's actually Falling For Innocence, mainly because I watched the trailer and it had nothing to do with the actual story, so I immediately disregarded it at first. Now it's one of my favourite dramas!
First, I would never start watching a drama I thought I would hate.  However, one drama I started out with very little expectation but it ended up as one of my all-time favorites is:  Dream High.
- Same here, I didn't expect much from Dream High because I'm not very fond of music dramas. But I ended up liking it thanks to Kim Soo Hyun. His role was so different compared to You Who Came From the Stars that I nearly didn't recognize him.
- I didn't expect to like Kill Me, Heal me so much even after a few episodes. I first rated it 7.5 but the more I watched episodes, the more the rating went up.
- And I was also reluctant to start Bad Guys until someone recommended it to me in another thread. It was really good.
Sungkyunkwan Scandal - I don't like historical dramas and when I first watched it, I did hate it. But after the third episode it got better and I ended up really loving it.

Cleopatra na Onnatachi - I was reluctant for the sole reason that this was a drama about plastic surgery. It sounded weird, it looked weird and I suspected it would be quite offensive. But it wasn't, it turned out to be amazing.

Sunao ni Narenakute - 100 % melodrama, which is the worst genre in existence. And nobody even recommended it to me! I randomly chose to watch it with absolutely no expectations. And I loved it.
Secret Garden, King2Hearts and Healer
I think there were a couple of k-dramas suggested by some friends that I have some doubts in it at first. One of them is the Moon Embracing the Sun. I'm not a huge fan of watching Historical dramas. Never liked it. This one is a total masterpiece! :) So many emotions..I cried, I laugh, I smile, I got angry, etc. I really loved it and may consider watching more historical romance k-dramas later. 
Ugly Alert
I watched part of the first episode and kinda said im not in the mood for this then about 2 months later a friend recommended it again
>It's okay, that's love 
I thought it would be cliche and it ended up as my favorite drama!
>Falling for Innocence
I almost dropped it at episode 1 but I continued and I really enjoyed it!
Secret Garden. TBH it took me a few try's to watch the first episode, but after that it was just hilarious and I loved it.
To the beautiful you - I thought I would dislike it cause I've never liked a gender bender drama before it and I thought the reason she dressed as a guy was very creepy. But the characters made up for all that and I found myself enjoying it more then I thought I would. 
Falling for Innocence. 
The heart transplant of deseased lover making them fall in love made me cringe.
I hate it when they fall in love with someone only because they remind them of their ex.
But it was a lot different then I expected. it wasn't ven makjangish but instead a nice rom-com with some serious scenes that 
weren't too much but instead made it more interesting. But still so much romance and comedy :D
This happens to me all the time with Jdramas. Like Real Clothes, I thought it was gonna be very cheesy but I ended up loving it! 
Love Shuffle: I'm not a huge j-drama fan so I was kind of scared to start watching it but it's been great so far.
Seonam Girls High School Investigators: I didn't think I would enjoy a high school-centered drama but it was interesting.
hahah I really thought I would hate It's Okay, That's Love, which ended up being my favorite korean drama. I also thought Dream High would be one of those, but it was another one I came to love.