PCIe over a short cable
What a coincidence.  I'm doing exactly that right now.  

There are lots of ways to do this, but controlling the impedance is critical.  The problem with using an unshielded ribbon cable is that it is hard to manage the impedance.  It can be done, but finding a good cable supplier is hard, especially one that can guarantee the impedance.  On the surface this looks like a good solution, but the difficulty of suppliers and stuff makes this less attractive.

Another way to do it is to use a shielded ribbon cable.  I don't like this approach because the cable is expensive and terminating the shield is next to impossible.

The Flex-PCB is a good solution, but the NRE is high.  If this solution is within your budget it might be the best thing.

A "quick and dirty and cheap" solution would be to use a couple of SATA cables!  The impedance is right, they are cheap and widely available, and more importantly they work.  Of course you will be limited in the number of signals so don't expect to get more than a PCIe x1 connection plus a reset signal (no power, JTAG, etc.).