An interesting article up at CBR about one of the ways Spider-Man's spider sense has been used and changed along the years.
Spider-Man having a heightened awareness of his surroundings, being able to dodge things whilst blind folded, or even know when someone is stalking him in some cases, that makes sense to me. It's a bit similar to Daredevil, but it makes sense - spiders are very good at detecting vibrations in the air and the ground. It's a super-power based on a spider's natural abilities. This is pretty much how the movies handled it from what I can recall.
But then there are scenes where Peter shakes an evil person's hand and is all "Uh-oh, spider sense tingling!", I just don't understand the logic behind that. It implies that Peter has some limited way of reading a person's thoughts. Similarly there are cases of spider sense telling Spider-Man which wire to cut in a bomb, which drink is the poisoned one and so on. It almost plays out like the "luck virus" from Red Dwarf! Too close to the realm of magic for my tastes, and it has absolutely nothing to do with spiders.