IDE is Integrated Drive Electronics. People use ATA and IDE interchangably. Basically when someone says IDE drive, they mean a drive with a 40 or 80-pin ribbon connection. IDE drives are slow, cheap, and the most common.
SATA is Serial ATA. It's new to the desktop scene. I don't know a whole lot about it as I really don't care, but basically it's a serial interface where IDE is parallel. The cable is much smaller, it's capped at 150MB/s (as opposed to 133MB/s for IDE). SATA tends to be a bit more expensive than IDE. They're still pretty slow, except for the Raptor which you'll hear about constantly here.
SCSI stands for Small Computer Systems Interface. It comes in 50, 68, and 80-pin configurations with 68 and 80 being the most common. With the 80-pin you don't need the 4-pin Molex power connector to attach to the drive. Usually a board with 80-pin slots on it is used and the drives are slipped into their drive bay where they dock with the board. SCSI has speeds up to 320MB/s, has command queueing (Basically the drive can store commands and execute them in a different order for efficiency). SCSI is very fast, often used in servers, and as such is much more expensive than either SATA or IDE. Setting up SCSI is a *little* more work, but once you know how to do it, you're fine. The cables are also very expensive, but they can stretch much farther than IDE cables. SCSI drives reach up to 15,000 RPMs and I've heard talk of 22,500 RPM drives, but I haven't seen any.