PCI-e is significantly different from the old PCI standard (and is in fact more based on AGP than PCI); one of the more visible differences is that PCIe has no parallel bus concept like PCI does.
PCI-e buses consist of lanes; one lane (x1) equals one serial 5gbit/s link between the host and the device.
These links are fully asymmetric and hence do not suffer from synchronization issues - this explains their far greater speed compared to PCI.
What is less visible but equally important is that the device and the host do not have to physically match the number of lanes they offer - a device with two lanes (x2) can connect to a host bus with 2, 4, 8, or 16 lanes on a single slot.
To further complicate things, the connector on the mainboard (the host bus or slot) does not have to actually connect every lane that will fit; an x16 slot can (and usually does) connect only 8 of the lanes, making it an x8 bus in reality.
These tend to be referred to as "x16(x8)" or similar.
So, to make the short answer to your question a lot longer: yes, you can connect any xN PCI-e device to an xM PCI-e host bus, as long as M >= N.