Firstly, the current drawn through the PCIe slot vary a lot depending on the card. Dual-GPU cards usually draw more than single-GPU ones (contrary to what someone said). Here are some of my own measurements with a clamp meter around the 12V lines of a PCIe extender, while Bitcoin mining:
HD 6990: 4.2 A
HD 5970: 4.1 A
HD 5870: 3.2 A
HD 6950: 2.5 A
HD 7970: 0.9 A
So for example the 7970 (and probably most other 7xxx series cards, but I have not tested them) draws so little power that they pretty much don't need powered extenders.
Also, eroxors, most of your cards are pretty low-end/mid-end. They likely all draw less than 3 Amp or so because your most power-consuming one seems to be the HD 5870 (3.2 A through the slot). Even if you had 4 of these cards, that's only 12.8 Amp total, so only 6.4 Amp per 12V wire of your 24-pin ATX adapter.
But most importantly, whether the 24-pin ATX connector overheats or not depends a lot on whether the Molex Mini-Fit Jr. pins in the PSU 24-pin plug have a single or double spring. You can tell by removing the pin from the plastic housing and seeing if it has one or two pairs of "dots" at the end. This one has two: http://www.alliedelec.com/images/products/Small/70090646.jpg The single spring pins (typically used by inexpensive PSUs) have a higher resistance and are more prone to causing the connector to burn out over time.
For example, in my farm of 4x5970 and 3x6990 machines from the old days, I noticed that upgrading from single-spring pins to double-spring pins pretty much made powered extenders unnecessary.
Finally, eroxors, you are right that the memory subsystem of Radeon cards (at least the 5xxx I tested years ago) is powered through the slot, not through the 6-pin or 8-pin power extenders. So Litecoin miners need powered extenders more than Bitcoin miners (at least for 5xxx and 6xxx cards, again the 7xxx series seems to draw so little from the slot, that powered extenders may not be necessary).
This makes sense as to why so many cards burnt up back in 2010/2011 and you see so few (so far none in 2013) now a days (on Bitcointalk). How many amps is safe to pull through the MOBO? Since you seem to be the only person able to acquire these numbers would be cool if there was a sticky with yearly updated information .
Im wondering if its safe to have 6 7950's on 1 board no powered extender.