iOS 4.2 and above have native WebSockets support.
For Android devices with Flash support (or any browser with Flash) you can use web-socket-js. Socket.IO actually includes web-socket-js as one of the transports that can be enabled.
See caniuse.com for an up-to-date list of browsers and mobile devices with native WebSockets support.
Update:
For native iOS applications (Objective-C) check out UnittWebSocketClient. One caveat: I looked in the code and it uses the HyBi-07 version of the protocol which is more recent than the Hixie-76 version currently supported by most browsers. However, if the server you are connecting to supports HyBi-07 or later it shouldn't be a problem.