What are the possible client-side architectures to access a local Smart Card from a generic browser (connected to a server through http(s)), preferably from Javascript, with
Update (8/2016): A new API for the Web called WebUSB API is being discussed. You can already use it with Chrome v54+.
This standard will be implemented in all major browsers and will replace the need for third-party applications or extensions for Smard Cards :-)
So the new answer is YES!
And the OSI-like architecture stack is:
2019 Update: As @vlp commented, it seems that it doesn't work any in Chrome because they decided to block WebUSB for smartcards for some specious reasons :-(
Note: Google annonced that they will abandon Chrome Apps in 2017.
Previous anwser:
Now (2015) you can create a Google Chrome App, using the chrome.usb API.
Then you access the smartcard reader via its CCID-compliant interface.
It's not cross-browser but JavaScript programmable & cross-platform.
Anyway Netscape Plugin API (NPAPI) is not supported any more by modern browsers. And Java applets are being dismissed by browser vendors.