Earlier this year at 44Café in London I did a talk in which I dropped about 16 bugs in SuperMicro's IPMI BMC implementation (through the medium of a drinking game), some of which were picked up by Farmer and Moore's recent research into IPMI, some not[1]. The Baseboard Management Controller (BMC) is a completely separate computer, often running unmaintained Linux firmware that has full South-Bridge and i2c access to your computer's memory. Basically it has Direct Memory Access (DMA) but your computer doesn't appear to going the other way around (although I haven't investigated this yet).
The board I looked at ran an ARM chipset and a custom Linux distro built by an OEM called ATEN[1] and customised by SuperMicro. It's not that the system appears to be phoning home, it's more that there are a lot of bugs and defaults in the implementation, and compromising this allows you to compromise the underlying server.
For desktop and laptop systems you don't usually have IPMI, so no BMC. Instead you have intel's iAMT which is very similar in some respects. There's some really fantastic research done in this space by Patrick Stewin and Iurii Bystrov[3] who have implemented a hardware keylogger. I've been in contact with them and they've updated their work since publishing the paper and intend to present the results at the 44CON[4] security conference in London this September.
Again it's not a case of these chips phoning home per se but a non-well documented nor well-publicised attack surface with real-world implications for espionage and malware.
Disclaimer: I'm one of the co-founders and co-organisers of 44Con.
[1] - http://www.wired.com/threatlevel/2013/07/ipmi/
[2] - http://www.aten.com/IPMI.htm
[3] - http://stewin.org/papers/dimvap15-stewin.pdf
[4] - http://www.44con.com/