Developers Cboomf and Felix 123 have released Wii Web Server, a new Wiibrew program that does what its name states. Spelled out, it's a web server for the Wii. Right now it's still in its early stages, but think of what it can do when fully developed. Perhaps a way to download Wiibrew straight to the console? Hmm... There's no readme so make sure you know what you're doing before you run the application. Here's the changelog from the website:

alpha v0.21

* Now detects the HTTP/1.x version as requested by the browser

alpha v0.2 - First fully web-page serving release

* Now serves a built in test page
* No longer needs telnet
* Forced use of HTTP/1.1

alpha v0.11

* Serves html to telnet (don't know why)
* Can accept multiple connections (not at once)

alpha v0.1

* Added Gamecube control menu control
* Added GRRLIB logo
* Added return to loader
* Opens port 80
* Opens a socket and allows for connection
* Accepts connection on open socket at port 80