When I say "influential drama" I mean a drama that influenced the story or style of many other dramas.

Hana Yori Dango: I think it imposed the tropes "School Life, Bullying, Rich Boys / Poor Girl, Love Triangle, etc" ... which was then imitated infinitely.

There is a first for everything, but for me the most "influential" is the one that makes that trope stand out the most and not necessarily have to be the best. Those I consider classics, an equivalent of modern-day Shakespeares' plays.

Boys Over Flowers / Secret Garden - rich male lead poor female lead / spiteful mother-in-law

Full House - celeb / love-hate couple

Ijimae - bittersweet / star-crossed historical love

Dream High - musical

You're Beautiful / Coffee Prince / To the Beautiful You - cross-dressing

 Playful Kiss - innocent high school love

Goong - royal couple

Hana yori dango franchise rich boy/poor girl-parents that are traditional when it comes to marriage
The manga came out in 1992 and includes the the following tropes

Rich boy poor girl
Spunky tough FL (or Weed Lead)
Angry on the outside, naive and squishy on the inside ML
Evil parent
Stranded on an island
Momento (had to think which trope the necklace falls under)
Love triagle

Theres more but I cant remember them all

I'd say that Scarlet Heart was pretty influential in the 'mc gets transported into the past' 'genre'.

Thanks everyone for the answers.

Can anyone give more examples of influential Japanese dramas and Chinese dramas (other than Hana Yori Dango and Scarlet Heart)?

Was Meteor Garden influential?  I haven't seen it, but I know it was based on the same manga as Hana Yori Dango.  I'm also wondering, what are the most influential wuxia dramas?

Meter Garden is influential, I think it's probably the most influential out of all the adaptations. I say that in terms how incredibly popular it was in East Asia and South East Asia at the time. It popularised the story even more.

For Wuxia, it'd always be Jin Yong's. His most popular works is Legend of Condor Heroes I think? Considering how many times it was adapted.  You can't really talk about how a specific version influenced dramas though because it's his novels that popularised and influenced the genre. Non Jin Yong well known wuxia dramas are by other well known wuxia writers from same time period.

Xianxia would be Chinese Paladin? which, again isn't the drama influencing other dramas but the original game (1995) creating the genre, and it was adopted and further popularised by web novels, which then got adapted into dramas. The drama is notable for amongst the first (2005) to be aiming for the younger audience. Previously most cdramas were more general audience/family kind of tv.