I am looking for a drama where there is the cocky/arrogant rich boy who falls for the sweet natured poor girl.The boy doesn't necessarily have to be rich. I have seen a lot of dramas but I would like some suggestions please. It can be Korean, Japanese, or Taiwanese. Thank you very much :)
Any of the Boys over flowers adaptations fit this.

Meteor Garden (taiwan)
Hana Yori Dango (Japan)
Boys Before Flowers (Korea)

Shining Inheritance (Korea)

So much more...
Honestly, pick any korean drama and it is probably of that genre. Especially if it Romcom, lots of times if it is melo. Just read descriptions...
Korean Coffee Prince Goong Shining Inheritance Taiwanese Autumn's Concerto (I didn't like it a lot, but many people do), Fated to Love you
All of these are Japanese.

Arakawa Under The Bridge: really rich, aloof guy has a chance encounter with a girl on a bridge. (best fits your description out of the three suggestions)

Natsu No Koi Wa Nijiiro: really rich, very cocky child of a celebrity/wannabe actor has a chance encounter with an older woman (she's not old, just older than him)

Ouran High School Host Club: Slapstick comedy about a poor girl at a school for really rich kids.
ikemen desu ne hotaru no hikari and if u want the opposite effect for what u asked. rich girl, nice poor boy then Tatta Hitotsu no Koi
Taiwan : Sonria Pasta, It Started With a Kiss, They Kiss Again Korea : Secret Garden, Greatest Love, a Millionaire's First Love
Thanks for the suggestions so far :)
Full House Invisible Lee Pyung Kang You're Beautiful My Girl.