Actually some airlines require a degree for you to be able to apply for a job.
Most of the airlines dont but as I said I know a few that do, so it all comes down to you and who you wish to fly for.
My personl opinion is that it should not be a requirement for you to get a job but I believe is helps you, if you have an aviation related degree, to look at situations and be able to judge them in a better way than a person that does not have a degree.
It also helps if you want to get involve in the management side of aviation.
CY