I’ve my computer connected to my speaker-equipped monitor through a DVI-HDMI cable. Audio through DVI is a hack, but it used to work until I upgraded from Lucid to Precise; afterwards there was no sound from the monitor. This is a regression introduced in Oneiric, due to the reverse engineered Radeon code causing issues in some setups. Thus upstream have figured it best to play safe and disable Radeon audio by default.
Luckily, it’s pretty easy to re-enable: add radeon.audio=1 to your GRUB_CMDLINE_LINUX_DEFAULT and run sudo update-grub.
Obviously, you’ll then run the risk of encountering the aforementioned issues.
Edit: Briefly after enabling, the HDMI audio again stopped working.
Edit 2: It’s actually flash audio that’s not working through HDMI as other audio is.
Edit 3: The flash problem was due to having an old flash package installed instead of one from the (Oneiric) partner repo.