AppleTV Airplay mirroring until Mountain Lion, Mac OS X 10.8 has only been possible for iPads, iPhones, and iTunes videos.
https://discussions.apple.com/docs/DOC-3761 tells you which Mac OS X 10.8 installed systems support Airplay.
This tip's bottom discusses also what cables you need to add an external display to a Mac.
Now Apple has made some modern Macs able to connect via Airplay with Mountain Lion. Look on this tip to find out which ones.
Note Mac OS X 10.9.2 currently has difficulty with Airplay, and is the only secure version of 10.9. Stay tuned to updates from this tip,
if you depend on it, or Airparrot, which also has some issues:
A software alternative which only now is known to be Snow Leopard, Lion compatible, is AirParrot. I've tried AirParrot on a MacBook Pro 3,1 with 2 GB of RAM and 10.7.3 and only had issue playing DVDs. It will just make the DVD playback into a checkerboard screen. Other software solutions I've not tried are:
For hardware alternatives, look below.
AppleTV 3 offered higher def video at 1080p, and 5 Ghz wireless.
AppleTV 2 and above support Airplay at 1080i and 720p. Mountain Lion support for Airplay and AirParrot listed earlier offer the ability to see the computer's desktop on a TV hooked up to the AppleTV.
AppleTV 1 and 2 offers compatibility with any video you can rent or own from the iTunes store.
They offer means of getting iTunes, or iPhoto (via iTunes) to either sync (on AppleTV 1) or stream (AppleTV 2) content to them.
They offer the means of streaming Netflix in stream queue (on AppleTV 1 and 2), and searching and selecting streamable Netflix content (AppleTV 2 only).
Both offer Youtube video support.
AppleTV 1 loses some iTunes store compatibility, with the advent of 1080p video. Many of the higher def videos are not available for the AppleTV 1.
All G5 and Intel Macs have had built-in DTS sound support. G5 iMacs have mini-VGA, wheras most G5 Powermacs had cards with DVI connectors.
All Intel Macs have at minimum mini-DVI if not full DVI support on the video side. G4 and older Macs unfortunately will not give you more than 2 channel sound.
AppleTV 1 supports Mac OS X 10.3.9 or later with iTunes 7.7.1.
iTunes 9.2.1 supports Mac OS X 10.4.11 or later.
AppleTV 2 supports Mac OS X 10.5.8 or later.
That said, several of third party wireless solutions support HDMI wireless up to 30 feet line of sight from your computer. Only the first one listed has been tested by the author of the tip. It takes some pairing time, and may interfere with Airport network if too many items connected, but it does work with DVD playback.
Macs which don't have audio over mini-Displayport connectivity, need either an
together with a Toslink to SPDIF connector to get full surround audio into the HDMI port after connecting through the Mac's compatible audio port and adapting to the compatible video port. Mini-DVI Macs can connect to the Apogee using this Protronix adapter for video if they are able to be a short distance away. Those with a mini-DVI port a longer distance away will need this DVI cable combined with this connector:
Note, only G5s and Intel Macs have digital audio. iMac G4s and some PowerMac G4s had a special minijack for stereo speakers that are no longer sold.
Note, I haven't tried any of these products except AppleTV 1, AppleTV 2, and the Nyrius as mentioned earlier.
Lastly, if you have an iPad with iOS 5 or later, any Youtube video you can view on the iPad can use Airplay to broadcast to an AppleTV 2 or later.
A related tip is: Can you make a Mac a second display to another?
Common video ports used by Macs:
HDMI ports are labelled HDMI.