While IDE adapters can be found on every motherboard for many years, you will have to specially purchase a SCSI adapter in most cases. A few motherboards are available with integrated SCSI-chip however. Those fully featured motherboards are clearly cheaper than a standard motherboard plus a PCI SCSI adapter card, but you can easily exchange the card if you want to upgrade to a faster or better featured one (e.g. multi-channel cards, RAID adapters etc).
IDE was born in 1984 in order to introduce a cheap interface for hard disk drives. IDE means Integrated Disk Electronic, which explains the basic idea: The controller chip is on the disk drive, not on the adapter (like SCSI). First IDE drive generations had been rather expensive, but mass production made the prices drop far below the costs for SCSI drives. IDE standards are updated on a regular basis, starting with programmed-I/O modes (PIO) 1, 2, 3 and 4, UDMA33, UDMA66 and today UltraATA/100 is the state-of-the-art standard for up to 100 MB/s of bandwidth. It is still downward-compatible; thus you can use every old IDE drive as well.
In order to keep up compatibility, the principle has never been changed. Two drives can be operated from one IDE channel. One is the 'master' drive, the other will be 'slave'. With the introduction of the ATAPI standard, CD-ROM drives could also be operated from IDE controllers. Therefore a second IDE channel became common, as attaching one hard drive and the CD-ROM would not have left any room for future upgrades.
The SCSI bus is both more complex and more flexible. Every device gets assigned a SCSI-ID number. It can either be set directly on the devices (using jumpers), or the host adapter assigns them. The most important advantage is the amount of supported drives: 8 devices can be in a SCSI chain, with one of the devices being the host adapter. Each end of the SCSI chain has to be 'closed' with a terminator to prevent signal reflexions.
All devices can also be operated externally. Some drives (e.g. Iomega Jaz) can be obtained as external SCSI versions. There are also special SCSI cases available where you can place hard drives, CD drives, streamers or other hardware. Also SCSI scanners are very popular due to the higher bus performance compared to USB or the parallel port.
Thanks to complex controller chips, SCSI is able to access all drives almost simultaneously, which is still not possible with IDE. Decent SCSI-adapters have its own processor and are able to do bus mastering, so that SCSI-bus tranfers don't cost any significant CPU performance.