The American Legion is a great organization for veterans. The provide community service, help with local and youth programs, and offer a friendly relaxed place for veterans to gather.
For me, the most rewarding part of being a member is to be able to rub shoulders with veterans from previous wars. It's a great benefit to be able to kick back with them, have a beer, and hear their stories.
If there is a veteran in your life who is not a member, consider the unique and generous gesture of giving them a gift membership. Here is a video from the national commandant explaining the program:
There are even opportunities for non-veterans to participate in the Legion Auxiliary.