1. Sometimes, the remake is so identical to the original that you have to ask "what's the point?"
2. Some artists will try to avoid that scenario by making such radical changes to the song that it becomes barely recognizable. And usually, that's a disaster.
3. Many artists fails to realize that their voice simply isn't right for a particular song.
As with all truths, however, there are exceptions.
A notable exception to #2 above is Chantay Savage's masterful reworking of the Gloria Gaynor's anthem "I Will Survive". One listen of this slow jazz version will abolish any notions of this as a disco song.
For situation #3 above, Sara Evans provides a nice antidote when she covers Rod Stewart's "My Heart Can't Tell You No". Her voice is so perfectly suited to this tune that it becomes obvious that Evans should have been the one who recorded this tune first. I can't take Stewart's version seriously anymore.