I actually do think the games are philosophical, in a way... like, a light touch, and mostly what the player brings into it, but since I'm a fanfiction writer who's brain is building upon everything all the time as I'm playing... here's a rundown of some of the philosophy and psychology various titles I've played...
Legend of Zelda Classic: The need of Wisdom to balance Power - specifically, it is a story about gaining wisdom before one can be entrusted with power. While it is done in the most literal way possible (you *collect fragments of the Triforce of Wisdom* ) I remember watching a special on either PBS or History Channel called "Rise of the Videogame" all about the origins of gaming in which Miyamoto, when interviewed about his creations, flat out said that was his philosophy behind the first Legend of Zelda.
The Adventure of Link: Gaining Courage by facing the dark side of your soul. Self-explanitory for those who've completed the game. Face your dark side or become it.
A Link to the Past: I remember doing research for an article that involved my learning of some of the copious Shinto themes this game has. There's also something to be said about facing your true self (how the Dark World twists people into the forms reprsenting their true selves) and the dangers of greed warping you, since if I'm not mistaken, it's implied that's how Ganondorf truly became Ganon the pig.
I have not played Link's Awakening... I suppose from what I've heard/read of it, it's a game that asks the very philosophical question "What is reality?" Basically the Matrix of Nintendo games?
Ocarina of Time: This game is about growing up. It's also a basic solid Hero's Journey, as they all are, but there's a lot to be said for the childhood Link missed and a child having to rapidly become a man because he needs to.
Majora's Mask: Oh, my goodness. (I vote this one as "most philosophical" out of the bunch). I have described this game (on my regular blog... when I was talking about playing it for the Mayan Apocalypse) as being about a fight against Nihilism. I see the dark desires of the Skull Kid, brought out by Majora's Mask and culminating in the falling of the moon as this mad suicidal rush by a party (Majora) who sees the world as having no meaning, something to end and Link standing up and saying "No! People and the world are NOT worthless!" (even those he does not know/has no connections to... and even those whose destiny is only to die). I find a lot about death and dealing with it in this game and also asserting a meaning against those who'd declare that there is none/who would throw it all away.
Yeah, my mind is weird. I've only ever played through the entire game once, too.
Oracles Series: The importance of nature and the courage to fight evil even if you may become destroyed in the process (I didn't find too much depth in these ones).
Wind Waker: The importance of the future and letting go of the past. Learn from past, but do not let it rule you, for there is a horizon you and future generations must meet.
I haven't played Phantom Hourglass yet...
Twilight Princess: Overcoming predjudice. Really! I know people like to focus on the Twilight and the darkness, but when I think about it, I think about how Link has to grudgingly work with Midna for common goals and how they both distrusted each other until they started reaching their goals together. We gradually see Midna's attitude soften and after the Lakebed Temple - well, I don't know about you, but my main concern wasn't regaining my human form, it was keeping Midna alive! You get the Gorons overcoming their distrust of Hylians after Link helps them, people being afraid of his wolf-form, even as he's saving them, and ultimately, we meet the Twili ... who, when not brainwashed and crazy are actually good (albeit strange) people.
Minish Cap: There are amazing things to be found in the world, even whole other worlds at your feet - if only you pay attention. (Okay, so this one's like the Oracles in that I didn't find too much depth in it, but hey, I'm trying!)
Skyward Sword: Love. Love and what one is willing to do for it. (And yes, this stands even if you aren't a ZeLinker... even if Zelda is just "a best friend" in your eyes, the love between friends is still a kind of love).
Spirit Tracks: Trains go Whoo! Whoo! (I haven't finished this one yet, I just started it. I'll look for a philosophy to it later).