Zhang Ziyi aka Ziyi Zhang

Equally-adept at comedy, drama, and action, Zhang Ziyi (or Ziyi Zhang, depending on the translation) isn't a martial arts expert, but, like fellow Fantastic Femme Michelle Yeoh (with whom she's co-starred twice), she uses extensive dance training to learn the needed choreography!
Next up, she'll be playing a live-action version of the legendary Chinese heroine Hua Mulan!
Trivia:
Didn't know any English when she did Rush Hour 2! She learned her dialogue phonetically and star Jackie Chan translated the director's instructions for her! (She has since learned English.)

Genre appearances include...
Mulan [2011] (Hua Mulan)
Sophie's Revenge (Sophie)
HorseMen (Kristen)
TMNT (Karai)
House of Flying Daggers (Mei)
Hero (Moon)
Warrior aka Musa (Princess Bu-yong)
Purple Butterfly ( Cynthia / Ding Hui)
Legend of Zu aka Zu Warriors [2001] (Joy)
Rush Hour 2 (Hu Li)
Crouching Tiger, Hidden Dragon (Jen Yu / Xia Long / Jiao Long)

Check out...
Her Official Site
Hello Ziyi (FanSite)

Other actresses to play Karai include...

Karen Neill in Teenage Mutant Ninja Turtles [2003]
Other actresses to play Hua Mulan include...
Wei Zaho in Hua Mulan [2009]
Ming-Na and Lea Salonga (singing) in Mulan [1998] / Mulan II / World of Mulan [2005]
Anita Yuen in Mulan [TV][1998]

Ming-Na Wen (Aanes/Zee)

Also known as "Ming-Na" or "Ming Wen", she has one of the more distinctive voices in the business, as shown by the extensive amount of animation voice-over work she's done in both tv and film!
Ming's demonstrated her acting chops in The Joy Luck Club and ER and her action prowess in the first Street Fighter film and Push (which is, ironically, opening shortly before the new Street Fighter film debuts).
Note: I complained about her lack of fighting ability in Street Fighter, but she has improved, as shown by her performanaces in Vanished and Push!
UPDATE: Ming's been cast as Agent Melinda May in Joss Whedon's S.H.I.E.L.D. TV pilot!

Genre credits include...
Agents of S.H.I.E.L.D. (Agent Melinda May)
StarGate Universe aka SGU (Camille Wray)

Push (Emily Hu)
Prom Night[2008] (Dr. Elisha Crowe)
Vanished (Agent Lin Mei)
Kingdom Hearts II[VG] / Mulan II/ Mulan/ House of Mouse (Fa Mulan)
The Batman (Detective Ellen Yin)
Spawn 3: Ultimate Battle/ Todd McFarlane's Spawn(Jade / Lisa Wu)
Final Fantasy: the Spirits Within/ Aki's Dream (Dr. Aki Ross)
Street Fighter/ Street Fighter the Movie[VG] (Chun-Li Zang)
Vanishing Son II / Vanishing Son IV (Mai)
StarQuest aka Terminal Voyage aka Star Voyager (Han)

Check out..
Ming-Na's Official Site
Ming-Na on Twitter

Other actress to play Fa Mulan:
Lea Salonga performed all of Mulan's singing to Ming's voice acting in the various Mulan films.
Other actresses to play Chun-Li include:
Kristen Kreuk in Street Fighter: the Legend of Chun-Li
Chingmy Yau in Future Cops
(and, no, I'm not going to list all the actresses who did voice work for Chun-Li's anime and video game appearances. You can Google them...)