I have heard of people fishing for really big TUNA!, Swordfish, baitfish, Humbolt Squid, and shark at night. Don't know that I'd want to handle a shark in the dark, though.
Edit: Page 83 and on in the Oregon Marine regs has the rules. There are a lot of species that are open 24 hrs. a day. Check it out here -->>
OR Ocean Regs