The original serial had 3, 5 or even 7 pins, but only one to carry the data.
The three pins serial worked like this:
The extra pin for a common ground is needed so that the other computer knows what to compare the data signal with. The receive and transmit lines are crossed, so that data transmitted by computer 1 is received on the receive pin in computer 2.
If you want you might call this two serial lines.
The 5 and 7 pins versions of the serial cables added extra signalling, allowing to signal when they where ready to receive data, or when they where busy (if busy, any data sent might be lost since the receiver had no time for it).
USB (versions 1 and 2) have multiple cables, but only one pair to carry the data signal. Hence it is a serial connection.
Look at this picture (courtesy of Wikipedia). You will notice two power lines, and one data pair (basically one line with differential signaling)
PCIe has serial lanes. Each lane transmits its data in serial form. A PCI-e connection with one serial lane is referred to as PCI-e x1, one with four as PCI-e x4 etc etc.
This has two reasons:
- Flexibility: It is easier to reconfigure mostly independent lanes
- Signal Skew.
If I signal data on multiple lines in parallel and the paths (cables+paths inside the device) are not of equal length then part of the signal might arrive out of sync. At high signalling speeds this was a serious problem.
Edit, as part of an answer to a comment. This is the pin-out for a PCI-e x1 connector. That one uses a signal lane on pins 16 and 17, but has many more connectors for other purposes (such as feeding power to the PCI-e card, signalling that a card is present etc etc)