I have a Zotac NM10 board with a full-length PCIe slot that is only x1 speed. It works fine for mining and there are no power problems, since higher-power cards (currently a HD5770) use separate power cables anyway. A HD5570 that draws about 40 W (no separate power) has also worked fine.
I have tried to use another GPU with an extender, since the mobo has another x1 slot, but it is normally under the heatsink of the first GPU. This did not work as expected, I could never get the total hash rate above that of a single card. I think this is due to other limitations in the mobo/CPU, since individually the GPUs work fine in their x1 slots, even with the extender.
An extender/riser may be a problem when the GPU is powered via the PCIe slot, but it should be OK for separately powered cards.
The Zotac is also my main HTPC, and when watching videos I simply use a higher -f setting for smoother playback. This slows down hashing quite severely, and I think a x16 slot does a lot better in these situations. But for mining only, the slowdown of a x1 slot is really only marginal.