FaceTime for Mac ($1) has an undocumented AutoAnswer feature ...
10.6: Enable AutoAnswer in FaceTime for the Mac - Mac OS X Hints
... defaults write com.apple.FaceTime AutoAcceptInvitesFrom -array-add +15205551212
... defaults write com.apple.FaceTime AutoAcceptInvitesFrom -array-add firstname.lastname@example.org ...
... defaults delete com.apple.FaceTime AutoAcceptInvitesFrom ...
The author used the "strings" command to uncover these options.
I've been looking for this for years  (die iChat die!), so, even though I generally avoid undocumented terminal entered preferences, I immediately set this up on my home iMac. I set it to AutoAnswer calls from my iPhone. Then I started up FaceTime and turned my screensaver on (screen is then locked) and placed a call.
With FaceTime on, a green light showed next to my iMac's "iSight".
The screensaver didn't change, but my desktop answered. My phone displayed the video input from the desktop and audio worked.
A few things to keep in mind as you test this ...
- Preferences are user specific. On a multi-user machine you have to enable it separately on each account.
- If FaceTime isn't running nothing happens.
- If the FaceTime window is showing the user gets a brief opportunity to cancel the call.
- If the FaceTime window is hidden it will answer, but there's no UI indication that a video chat is working.
- You can configure FaceTime to run on startup.
I'll be testing this out over the next few weeks, then I have to see if I can persuade my elderly parents that this is something worth enabling on their Mac. It would require an upgrade to 10.6, I think I'd left their machine on 10.5.
For an elderly user, or for anyone who wants a very simple way to create call you can create clickable desktop shortcuts or links in a web page ...
In Safari's address bar, type in one of the following URLs:
- facetime:// appleid
... select that URL in the address bar and drag it to the desktop.
When you do this you get a very dull file. Use IMG2ICNS (Free) to turn a photograph of the person you want to call into the file icon. I did this for my mother then put the icon with my picture on her desktop.
 Google could never come up with a decent control UI for Google Video Chat.
- Video Chat for elder parents over OS X: Google Video/Gmail, Google Notifier, Firefox and LogMeIn (4/2009 - a kludge that sort of worked)
- iChat - weirdest computer experience (2/2009 - iChat was really bad)
- User image propagation from OS X desktop to Gmail via iChat (2/2009)
- Apple's iChat (videoconferencing) problem (12/2008)
- Can't select Jabber or Google Talk for iChat? Here's one reason (5/2009)
- When a feature really is a feature: iChat AV's mirror mode (10/2007)
- The dead quality desktop webcam market (8/2007 - before the Logitech)
- Microsoft LifeCam VX-7000 vs. Logitech 9000 and VisionPro -- it's in the focus (12/2008)
- Logitech QuickCam Vision Pro webcam for OS X and XP: I love it (2/2009 - first really excellent and successful quality webcam. Still the best.)
- How: Automated XGA resolution JPG USB image capture at rate 1 FPS (webcam?) - rec.photo.digital | Google Groups (a 2003 usenet post of mine - for historical reasons)
- Streaming video over the net - Quicktime, Ustream.tv and Watershed (3/2009 - wow, I've tried everything)
- DIY video baby monitor and video broadcast review (7/2009)
PS. When reviewing some of these old links, I was struck by how many years we've been trying to get useable 1:1 videoconferencing on the net. We're talking at least 13 years of repeated failure, with only modest recent success with Skype and Google Video Chat. Apple has failed repeatedly. I wonder if this time they'll push it through, but I've thought we were close before.