50 pin is the original SCSI connector, 8 bit data transfer and pretty slow transfer rates. The cable is like a big IDE cable.
68 pin was originally introduced with Wide SCSI to give 16bit data transfers and a higher density cable. This connector is the most common not only because it's faster but it takes up less space on the drives.
80 pin is also known as SCA and is used in servers to provide hot swap capabilities by integrating power and data into a single connector. SCA drives also don't have the jumpers to allow you to set the SCSI ID (each drive on a cable must have a unique ID), the ID for SCA drives is set on the hot swap backplane. The signalling is identical to 68 way SCSI and so adapters are widely available to breakout the SCA connector into a 68 way and a molex power plus DIP switches to set the ID for the drive.
You'll see a lot of 80 way drives up for auction second hand in server manufacturer's caddies, these can normally be removed easily to let you use the bare drive in your own PC.