I think you're asking whether your external drive (or enclosure in which you mount your own HDD) should have its own power supply. By the way, they come in three forms: a "wall wart" that plugs directly into the outlet; a box with one cord to the wall, and another to the enclosure; or, a simple cord from wall to enclosure, with the actual power supply circuitry inside the enclosure.
Personally, I prefer to have the power supply unit come with the enclosure. In practice, it's hard to avoid that. Virtually ALL 3½" HDD units (the common size for internal drives) use too much power to draw from a USB port which has a limit on how much it can provide. In those cases, almost no external drive or enclosure will even try to rely solely on the connection to the computer for power - they will come with their own. Now, among smaller units usually sold for use with laptops and built with a smaller HDD inside, some can be powered within the USB port limits and they do NOT come with a separate power supply. A few like this use a trick to get power: the cable to the computer has two USB connectors on the end, and the second one is only to plug into a second USB port to draw more power.
As I said, I prefer that the external drive have its own power supply so it does not load the computer and its ports. Among the three types I noted above, I least prefer the type that has it inside the case - that just adds to heat generation inside the case and therefore adds to cooling demands. An external power supply leaves only HDD unit heat to be removed to keep the HDD cool.
There are three common types of interface between computer and external drive. By far the most common is USB2, and those ports on a computer do have limited power available in their design. However, this is the slowest interface of the three common ones. (The new USB3 system is MUCH faster if it's available to you.) BUT, these USB2 ports are on virtually EVERY computer. A faster interface is eSATA which can be just as fast as an internal SATA connection. As originally designed, eSATA has NO power available in the port, although there are new re-designs that have power in the eSATA port. The third common one is IEEE 1394a (aka Firewire 400) which is almost as fast as eSATA and does have some power available in the port connector. (The faster version of this latter is IEEE 1394b, aka Firewire 800, but it is uncommon on PC systems.) It is VERY common to find external drives and enclosures with two of these, or all three. My own is an AZIO enclosure with USB2 and eSATA ports and its own power supply in a middle-of-the-cord box, containing a Seagate 500 GB HDD.