In the original Marvel comics, Peter Parker was bitten by a radioactive spider. The spider, erroneously termed as an insect in the original comics, was hit by and absorbed an extraordinary amount of radioactivity. It bit Peter Parker, who was the nearest life form in the exhibit room.
There is no definite explanation regarding the class or species of the spider that bit Parker. The comics only hinted that the spider was close to dying after being exposed to radiation and transferred a proportional amount of strength and agility to the comic's protagonist. In the July 2014 chapter of the Amazing Spider-Man, however, the possibility is introduced that the spider may bite a person other than Parker.