The original version of the Gilligan's Island theme song was recorded by The Wellingtons.
According to "Here on Gilligan's Isle", the second (and third) season version of the song was performed by a group called The Eligibles.
User "supercat" asked in a comment on this question:
Do you know if the Wellingtons demanded a per-show royalty, or if there was some other reason they were used for the first season but not the second? Until I watched the show on DVD, I would have guessed the later theme started in a lower key; I was surprised to find the difference stems purely from the different singers' voices.
Why weren't The Wellingtons used for the later season recording(s)?