Here's my OPINION on the subject.
All-wood bows (laminated or self bow) should be unstrung when not in use.
Glass-laminated bows can be left strung forever. However, here in MI it is illegal to transport a strung bow unless it is in a case, therefore you'll probably want to unstring it a goodly amount of the time.
No bow should be left strung in a hot car, truck, room, etc.
Longbow or recurve makes no difference.
Storage should be horizontal on pegs as mentioned above. I don't believe it matters if they're hung from the string or on the limbs, but store mine unstrung supported on the limbs. You can get more on the rack that way.