Please recommend your favourite Taiwanese dramas~ especially dramas close to classics like 'Drunken to Love You' , 'Devil Beside You' , ' Why Why Love' , 'It Started with a Kiss' , etc!

Thank you! 

Mars
Fated to love you
Sunny Happiness
ToGetHer
Bull fighting
My lucky star
Just You
Love keeps going
Sunny Happiness
You are the apple of my eye - movie
Just You
Behind Your Smile
The Way We Were - probably the best tdrama I've seen.
Marry Me, or Not - kudos for the hottest scene in all of drama lol.
+1 Office Girls - Watch this for Patrick Lee, he's LOL
+1 Sunny Happiness - Mike is good but the actress is fantastic

My favorite Taiwanese dramas:

An Innocent Mistake (my fave)
In A Good Way 
Bump Off Lover
Drunken to Love You 
I agree with Bump Off Lover. It's unusually dark for a twdrama (the recent ones, anyways) and it has substance anda nicely rounded mystery.
Autumn's Concerto-It's a sad drama
Love or Spend-BFFs who live close  to each other and work in the same company
Fated to Love You- I believe Drunken to Love You is kind of like a spin-off of this drama
Not sure if it's exactly like the dramas you mentioned above but try

Someone Like You
Down With Love