As Estellios pointed out, any fish that has "Crafting Material" in its tooltip can be used in some recipe or another. Fish such as Dusk Gobies, Dark Bass and some other can be crafted into bait. There's also fish that can be Mooched to catch larger fish, but only certain ones of those can be used.

HQ fish are worthwhile to have as your Grand Company turn-ins will reward you 50% extra XP for them if you turn in all HQ for what they're asking. They also boost your starting quality for any of the fish that are used in crafting recipes.