The number one reason to join a fleet would be community. A place to chat about interests without having to deal with some of the things you see in zone chats (ughh). And with a large and active fleet you can get queue support during special events (looks like the crystaline entity is scheduled) rather than depending on a pick-up-groups.
The secondary reason would have to be for the loot unlocks. There's some pretty nice equipment (ships, consoles, BOffs/DOffs...) to be bought requiring fleet credits earned by contributing to a fleet as well as upgrades (more DOffing and R&D slots, refining dilithium assignment...) and specialty costumes.
Definitely what fftt says. With a good fleet you will have other players to help you out when you need it like running STFs for marks or teaming up for a story mission you're having trouble with. Also, the equipment you can buy is nice. Some of the fleet consoles are must have and fleet weapons are nice until you can craft better ones. There really isn't a downside as long as you pick the right fleet that is a good fit for you. Head over to Earth Space Dock or Q'onos sections of the Feedback forum depending on your faction and read through all the posts till you find a fleet you want to try.
Comments
The secondary reason would have to be for the loot unlocks. There's some pretty nice equipment (ships, consoles, BOffs/DOffs...) to be bought requiring fleet credits earned by contributing to a fleet as well as upgrades (more DOffing and R&D slots, refining dilithium assignment...) and specialty costumes.