Not so long ago one reason to use packed sprites instead of seperate ones was that graphics hardware was limited to power-of-two textures (256, 512, 1024, ...). So you would waste a good amount of memory by not packing the sprites as you would have to enlarge everything to power-of-two dimensions before you could upload it. Packing multiple sprites into a single texture worked around that.
Another reason is that its much quicker to load one big image file from the HD then it is to load hundreds of small ones. This is still the case as file access comes with quite a large overhead per file, so the less files you have the faster things become. And especially with small sprites you can easily turn hundred files into a single one, so the saving can be quite noticable.
There are however also reason against having everything in one texture. For one OpenGL is no longer limited to power-of-two textures, so any size will work. But more importantly, packing everything in one texture has negative side effects. When you for example have lots of scaling in a game you have to be careful about the borders of your sprites, as colors will blend into neighboring sprites giving you ugly artifacts. You can avoid that to a certain degree by adding extra space around your sprites, but its not a perfect solution. Having everything in one texture also limits what you can do with the image. For certain effects, such as a waterfall for example, you might want to do the animation by simply offsetting the UV coordinates of the texture, you can't do that so easily when everything is packed into a single texture.