You can hunt hogs 365 in Arkansas and hunt deer 5 months out of the year..

 
  Mountain Lion is open year round in Oregon, units have quotas but are seldom met. No hounds.

Mississippi and Louisiana 

Arizona, looks like rabbits and fur bearing predators like yotes are all I could find in current reg book. I don't count sparrows and some other birds as game animals

Here is what I have so far.....

AR

AL

AZ

CA

CO

GA

ID

IL

KY

LA

MI

MN

MS

MT

NC

NY

OK

OR

PA

SC

TX

WY

Don't forget Alaska.  There are many interior units where black bear season is open year round.  A few units with grizzly open year round. There are also resident areas where caribou is open year round.  Also units with beaver and coyote having no closed season.  The reality of hunting year round here isn't terribly practical as the state is so huge and really I get enough adventure each year that I need breaks to regroup for the next one anyways!   A bit different than driving down the road or even just driving a few hours to another area of the state to hunt.

Thanks Ben, adding it now....


AK

AR

AL

AZ

CA

CO

GA

ID

IL

KY

LA

MI

MN

MS

MT

NC

NY

OK

OR

PA

SC

TX

WY