External hard drives have become a very popular method of expanding your computer's storage capacity, but despite this convenience, they also can become a cluttered mess. I've seen users attach numerous external drives at once, with webs of daisy-chained drives connected through various hubs and keyboards as well as being directly connected to the computer.
With these setups, and even with simpler ones with only a few devices, people have reported some of the drives in the chain unmounting and giving a system error even when they are not the ones being accessed. This may happen randomly as well, though usually when a file is opened or when a system service like Time Machine needs to access a drive.
Technically with USB and Firewire devices, any connection setup should work for external drives since you can have up to 127 items on an individual USB bus and 63 on a Firewire bus (though only 16 daisy-chained in series); however, in practice when items are connected in series there are other limitations and cautions.
The first is power. External drives may require their own power, or have the option to run off the Mac's power. While bus-supplied power is convenient, especially for notebooks, it has a limited capacity and should only be used to reliably power one hard drive device at a time. Usually bus power is best for the smaller portable drives that use 2.5-inch notebook hard drives in them, so if you have a large drive that contains a 3.5-inch desktop hard drive, then be sure you have it connected to external power.
When drives are daisy-chained, they all will pull power from the same bus. If you are at the limit of what the bus can provide, then when the drives are idling, they may appear fine. But when you access one it will draw more power and cause the other to fail. If the failing one is the last in the chain, then it may be the only one to unmount, but if it is the first in the chain, then all the drives could unmount.
Because of this, the second caution is to avoid daisy-chaining drives unless it is necessary. While daisy-chaining should work in theory, doing so results in every drive in the line being dependent on the ones before it. If one loses power, then the others may also lose their connections to the computer. Additionally, if one is having firmware problems or other incompatibilities then performance may also suffer. Be sure to connect as many drives directly to the computer as possible, and if you absolutely must expand the number of USB or FireWire slots on the computer then consider using a hub with dedicated power instead of daisy-chaining the devices.
Lastly, choose the Mac version of devices if possible. Even though Firewire and USB controllers should be universal in nature, some are tweaked to work with Windows machines and are not supported on the Mac. If a manufacturer sells a Mac version of the same drive model, then you may need to use that one if the controllers are different. Sometimes manufacturers sell Mac versions that are the same device formatted to HFS+ and mark up the price a little because of this difference. Unfortunately there is sometimes no easy way to tell if this is the case, but at least the drive is supported on the Mac.