I was thinking the other day my only real exposure to HK cinema is Jackie Chan, which don't get me wrong, is some of the best but I'm curious about what else the region has? Bonus points if it has Michelle Yeoh in it because she's cute 
OK, kind of a big list incoming...
Basically any Wong Kar-Wai movie except for Blueberry Nights (his only US film) & his wuxia movies. All his movies are about his deep relationship with Hong Kong and it's history, character, and psychogeography. Usually with the help of cinematographic genius Christopher Doyle his movies are unremittingly beautiful (although not always glamorised) visions of HK. Some good ones to start with might be... -In The Mood For Love: two broken people find comfort and connection in a visually stunning 60s HK
- Chungking Express: two mirrored stories about romance in one of HK's more 'underbelly' neighbourhoods in the 90s -Fallen Angels: two thematic stories of loneliness & alienation within the criminal/underclass of HK, with a darker tone & palette but just as amazing visually as the other two
Everybody knows John Woo, especially after his successful but less brilliant Hollywood stint, but his HK classics are still genre staples for a reason...
- The Assassin is really the blueprint for his morally complex HK action hero archetype and his bombastically stunning visual & choreographic action style. Hard Boiled takes the action up a notch further and is relentlessly entertaining as 'gun-fu' movie.
- A Better Tomorrow has some more complex characters and themes, following a criminal who goes to prison and comes out to find the world and the people he knew have changed but not without new problems.
- Bullet To The Head is perhaps the most thematically and contextually interesting as it follows a group of friends all made and scarred to various degress by their experiences during the war on Vietnam and is very much a movie about the ongoing violence that the experience of war inflicts on everyone.
JohnnienTo's Election 1 & 2 are great HK gangster movies that, whilst containing bursts of brutal violence, are incredibly detailed looks at how the organised crime structure works and is influenced by the powers in society, whilst also having a good amount of satire about both the mainland and the shallowness of the West's capitalistic-driven ideas of '"democracy". All through the narrative of a Triad organisation election as the HK handover looms. Any of his 80s hero movies or 90s gangster classics are worth a watch too, but this double feature is the most interesting (and different) of his newer stuff.
Infernal Affairs is the modern HK crime epic that Scorsese just outright remade for The Departed, but honestly the original is superior in my books. It's tenser, quieter, has more depth and less Boston accents. The sequels are good too and expand the backstory and side characters, but not essential.
Mad Detective is a bold, brilliant, and very ungeneric crime movie about an apparently insane former detective, who claims he can see people's inner demons, trying to crack a case. It's very much a psychological drama wrapped up in the genre stylings of a neo-noir detective plot.
If you don't fancy more crime films (it's a lot of Hong Kong cinema in general and even more of what gets released elsewhere)...
House of 72 Tenants definitely feels old since its from the early 70s, but based on a comedic play from the 40s, but when I last saw it you still couldn't go wrong with a story of solidarity about neighbours trying to turn the tables on the villains of landlords and corrupt law enforcement.
A Simple Life is a gentle and warm slice of life intergenerational drama about an elderly former housemaid being cared for now by on of the son's of the family she worked for. It's sweet, sentimental, lightly funny, not too heavy handed, and has a fair amount of class and generational politics just beneath the surface.
For just enthusiastic embracing of cartoon fight choreography and wacky fun, Shaolin Soccer and Kung Fu Hustle are both thoroughly entertaining, deeply deliberately silly early 2000s comedy watches.
While I'm not particularly big on Hong Kong horror really, there's a couple of non-generic ones that might be worth looking into.
Mr Vampire is probably the reason you have come across the myth of the Chinese hopping vampire (assuming you have) as it took an old idea and repopularised it in this 80s horror-comedy that I remember being brashy bizarrely great fun.
Stephen Chow's Out of the Dark is a genuinely comedic 90s horror where he plays a former mental patient turned ghostbuster who teams up with a little girl and some building security guards to get rid of evil spirits. It sounds a bit Ghostbusters but it's actually kind of a parody of Luc Besson's Leon: The Professional.
A double bill I was considering revisiting this October for the first time since they were new is Tales from the Dark 1 & 2 because I love horror anthologies/vignettes and whilst I remember the quality of the individual stories being uneven they're movies that are very much about Hong Kong as a city throughout the decades as much as just spooky stories.
There's almost definitely more, but I've been typing too long and it's getting late here.