Now that Google Chrome 11 has hit the beta channel, you can expect to see extension and Web app developers making use of the new HTML5 speech-to-text API. In fact, there's as least one slick extension you can already install: Speechify.
Install Speechify, and you'll see a microphone icon added into the search box on many popular sites -- like Google and Bing. Click it, and Speechify will convert the words you speak into text. You've still got to press enter or click to search, and an automatic submit option is definitely something we'd like to see added.