There aren't really that many candidates to consider, since the last twenty years has seen such a dramatic change in the action movie genre. There are guys now (Matt Damon in the Bourne films, for example) who I think are very good in action roles, but who I wouldn't necessarily consider "action heroes" in the same ilk as Schwarzenegger, Stallone, or Willis (Die Hard was released in 1988, by the way, making him an action star more than 20 years ago).
There are also a lot of names that American audiences are relatively recently aware of, like Jackie Chan and Jet Li, but who've been working, and hugely popular, in China for decades.
So, thinking purely of "action hero" over the last 20 years... Nic Cage was headed there for a stretch, but his work in comedy and drama has always been stronger so I can't quite go with him. Vin Diesel had promise (Pitch Black still rocks my socks off), but he took himself way too seriously and seems to have dropped off into obscurity.
The obvious choice, I think, is Statham.