I'm looking for a video surveillance system with the following features:-

1. Low cost video camera (<US$250) that will make a dial-up connection
via built-in or external PSTN modem when triggered by an external
event (volt-free contact or TTL signal) and start streaming video and
audio to the PC.

2. Corresponding client s/w for remote PC that will automatically
answer calls from remote cameras and automatically display and record
the remote live video images without human intervention.

Wish list and notes:-

1. Client s/w able to handle multiple calls simultaneously, via
multiple modems at remote PC.
2. Client s/w which is open source, or has APIs to interface with
other applications.
3. Being limited by dialup modem speed, low video/audio quality is acceptable.
4. If the system comes with IP/LAN connectivity, it's a plus, but
dialup connectivity at camera site is essential.
5. Instead of point to point dialup, a camera that dials up to a
webserver is acceptable, provided that client PC can receive live
video/audio via the webserver through broadband connection.
6. Essentially, the challenge is to find an event-driven camera system
that will work without a LAN connection at site. On the client side,
main requirement is an automatic display and recording of live
video/audio when event is triggered. Client connectivity can be point
to point or through the web.

Referenced sites:
1. http://www.3jtech.com/ - Model CAMit I & II+ not suitable because
there is no audio and client s/w does not automatically display video.
User has to manually playback recorded video.

2. http://www.axis.com - AXIS 2100 or similar models - Modem
application allows only FTP sequences but no live video/audio streams.

The best product that I have found on the market at present is by "Swann".
a complete package with 4 cameras can be purchased for about $600 US. 
The package includes:
Night Vision, Motion Sensing, Recording to computer Harddrive,
automated alerting, wired or wireless camera connections, internal and
external cameras, support of up to 16 cameras, as well as Wall mounted
or Hidden or mobile cameras.  You can get more detailed information at
the following link http://www.swann.com.au/show_cats.php?maincatsel=Security

Thank you for input, but it does not meet my requirements - which is
basically a camera with dial-up modem

Hello pouncer, 

I think what you need is a remote surveillance system. This is what you will need. 
1. Camera
2. Cables, transformer, power, etc.
3. Computer with video card (Capture card)
4. Surveillance software
Usually, the way that I have done it is, set up the camera and run the
video fee into the video card. The video will then be captured onto
your surveillance software. Since your computer is setup as a
webserver, you come pretty much monitor it from anywhere with internet
connection. A lot of systems out there offers up to the moment video
streaming.

Google search should solve fine you some good prices.