I couldn't find an option for that, though it should be possible as far as I understand e.g. http://www.techradar.com/news/internet/youtube-adds-automatic-subtitles-for-the-deaf-674860
AFAIK voice recognition and transcription is done on some videos, apparently chosen by Google. An example of such here. For videos that are transcribed, there is a button to activate it next to the quality button in the lower right corner, look for the two "c"s†. Click "Transcribe audio" to activate it, and open the menu again to activate automatic translation.
If you wanted transcription of something somebody else put on YouTube, I'm afraid you'll have to wait until Google decides that is what they do.
Apparently, things have changed since I looked closely at YouTube the last time. However, it appears Google chooses which channels they want to run full text-to-speech for, but any producer can upload transcripts themselves and have timecodes generated automatically. You can do that on the "Captions" tab of the settings page for the video you uploaded.
† Not from original author: Icon design may have changed since the above was written, see.