Google has introduced a way that you can talk to your browser, as long as that browser is Chrome. It won't talk back, but it will do your bidding. These instructions cover the basics of the new speech-to-text feature, which is functional but has yet to be implemented widely.
Use speech-to-text in Google Chrome
First off, be sure that you're using Google Chrome 11 (download for Windows | Mac | Linux)or later, and that you've got a microphone. Next, you have to navigate to a site that supports the new speech API. Currently, that's limited to Google Translate, which itself is limited to translations that originate in English. Expect that to change as site developers begin to implement the feature. One other hitch is that because this is a brand-new feature, it's also limited at present in Google Translate to translations originating in English.
So: Set Google Translate to English, then click the microphone that appears in the lower right-hand corner of the input box. Speak the sentence you want translated. When you're done talking, Google will automatically translate it. You can also use the site's Listen option (to the right of the text field) to hear what's the translation sounds like.
Web sites that currently use the speech API
Web2Voice, which demonstrates embedded video playback, control, and search
HTML5 demo Web site
There are currently some unofficial options for playing with the Speech-to-HTML API. The Web2Voice site that I discovered in a Chromium HTML5 Google groups forum has implemented basic YouTube compatibility using the new speech API. Click the microphone icon and say, "Green Lantern trailer," to search for trailers from the upcoming movie. If you click and say, "Play official trailer" it will play the trailer with those words in the title. To pause it, click and say "stop." To resume, click and say "play."
This isn't an official implementation, since that would appear on the YouTube site. But this certainly gives a strong indication of what the API is capable of. Unfortunately, having to click the microphone for every input is a bit of a pain. You might as well just click the pause button yourself. Also annoying is that the feature has trouble distinguishing between audio playback from the computer and your voice.
What this likely will be extremely useful for is accessibility within the upcoming Google Chrome OS. If you're spending you're entire computing time in the browser, as you will be in Chrome OS, and using the keyboard isn't easy for you, then having on-demand speech-to-command options are a must.
If you discover more options for the API, let me know in the comments below.