Valeri Lilov defines the following as Unorthodox Chess Openings:
- Sokolsky
- Dunst
- Double Fianchetto
- Richter-Versov
- Anderssen, Larsen, and Grob
- Fantasy Variation
- Chigorin Variation
- Center Game
- Danish Gambit
- Blackmar-Diemer and Omega Gambit
- Nimzowitsch Defense
- Hippopotamus
- St. George
- Gurgenidze Variation
- Balogh and Kingston
- Latvian, Elephant, and Greco
- Chigorin Defence
- Albin's Countergambit
- Budapest Gambit
- Tango
- Polish Defense and Englund Gambit
Some of them are perfectly playable. Any well researched unorthodox opening can be an affective weapon against the unprepared.
Tony, I disagree with you there. A line that is out of fashion (For example, the Ruy Lopez Exchange Variation is not common at high levels of play due to its drawish nature) is absolutely not "unorthodox". Unorthodox means openings which are almost never seen due to being generally regarded as junk (the Englund, the Latvian, anything named after an animal except the hedgehog). There's also another category of dubious openings which occasionally resurface but should not be a first option, such as the King's Gambit, the Albin Gambit, or the Danish Gambit which aren't good compared to normal openings but for some reason are still kept alive.