The most popular interface used in modern hard disks--by far--is the one most commonly known as IDE. This interface is also known by a truly staggering variety of other names such as ATA, ATA/ATAPI, EIDE, ATA-2, Fast ATA, ATA-3, Ultra ATA, Ultra DMA and many more as well.
The most commonly used name for this interface, "IDE" is a misnomer itself. The "proper" name for the IDE interface is AT Attachment, or ATA.

The invention and development of this interface catapulted hard disks into a new era of performance, reliability, and compatibility. IDE/ATA hard disks are used on the vast majority of modern PCs, and offer excellent performance at relatively low cost. They are challenged only by SCSI, which has certain advantages and disadvantages when the two interfaces are compared..
In fact, rather than a challanger, SCSI and IDE systems are 'at home' together.

In terms of its basic operation, the IDE/ATA interface is fairly straight-forward, and also reflects its origins as an extension of the ISA system bus. The connection between the system and the hard disks is 16 bits wide, so two bytes of data are passed at a time between the system and any hard disk. This is true regardless of the width of the system bus, and persists even today with high-performance enhancements like Ultra DMA. Two drives are supported on each IDE/ATA channel, with special signalling used to ensure that commands sent for one drive don't interfere with the other.

Note: In the early days of IDE, there were two other variants on the IDE/ATA interface, that were not compatible with regular IDE/ATA. One was an 8-bit version intended for use on the ancient 8-bit ISA bus of the first IBM PC/XT machines and clones. Another was a 16-bit version designed for IBM's MCA (MicroChannel) systems. Both of these have been obsolete for a decade or more and are no longer seen in modern systems.