You bought a Maxtor drive? Send it back before it catches fire. I've had six of them fail on me over the last decade (compared to not a single of over a dozen Western Digital drives), so I don't trust them at all. This is where everyone tells me about how reliable their Maxtor drives have been, I bet.
More commonly an indication that it's already completely fucked. The one time I've run into this on a working drive, the drive lasted, although the read/write speed was atrocious. Either way it isn't right, and it needs to be returned.
The distinction is pretty cut and dry - 2.5" (laptop HDD) based external drives can be powered from USB's 5v line alone (unless they're really shittily made), 3.5" external drives require external power (I presume it's a 12v line).
Chicky external drives is not something to be very worried about unless it is excessively loud or Windows is having issues accessing the drive, especially if it is a 3.5" drive inside the enclosure. If performance is nice and fast but you hear it accessing the drive then this is is probably just down to the model you bought. I handle a large number of external drives of various brands in my line of work and there is no sure sign that noise = impending doom. So hopefully that eases your mind somewhat. Ethernet is only 'self powered' if it supports PoE and is connected to a device that supports PoE. For USB there are various options, as Alchy says - 2.5" based externals usually power from USB input, some 3.5" and 2.5" drives power from an additional USB cable (they have two USB cords to the computer), some require a power cord. E-SATA (fastest connection) usually require a power cable, but I have seen some that use a USB cord to power themselves also.