Are there any ongoing projects trying to develop a widely accessible WebCL-powered mining software? I've heard of two in the past, but their websites don't seem to be working any more.
While not directly a WebCL miner there is a miner which uses OpenCL via Java Webstart so is accessible to any internet user with Java installed and apropriate hardware.
The site is both a pool and a custom java miner. The pool can be used with other miners however the BitMinter miner works only with the BitMinter pool.
So let me summarize all the other answers:
Krad Miner used to be the first WebCL miner, but due to DDOS attacks it was not working for awhile. Later it was bought and open sourced as Tumen Miner.
BitMinter allows you to mine on their pool with OpenCL miner through Java Webstart.
www.coined.com has undefined status, WOT reports it as an abusive site.
WebCL bitcoin miner looks like a fully functional WebCL miner
Bitcoin Plus allows one to mine through a Java Applet, but it is a (highly inefficient) CPU miner.
And there are a couple other less notable web CPU miners.
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There is a page claiming to be an OpenCL miner at coined.com but I'm not sure if it's functional or not.