I know I'm repeating a lot of what's already been said here, but I just have to chime in on this one.
The Atmosphere: Absolutely (IMHO) can not be beat anywhere. They do such an excellent job of immersing you in the feel of the tropics that it's like a vacation within a vacation. The tiki-torch lined paths, lush vegetation, Hawaiian music, sounds of the waterfalls (pool and GCH), the longhouses (as opposed to a giant hotel) and the cast members all combine to make you feel like you're really far away from everything.
The Location: Sitting directly across the lagoon from the Magic Kingdom makes the Polynesian that much more magical. It makes me feel like I'm truly in the "heart" of WDW. Viewing the fireworks from the beach (or your own balcony, as we have been blessed to be able to enjoy) is a great way to enjoy them without dealing with the crowds. If you're out early in the morning, you can listen to WDW come to life. Hearing the first boat horns of the morning on the lagoon and the music from the Magic Kingdom starting up, and watching the first monorails of the day glide around the lagoon is just awesome.
Location Part II, Transportation: The transportation options are unmatched. You have the boat and the monorail to get you to MK. You can take the monorail around to the TTC or walk there to get the monorail to Epcot and the bus to AK or DHS, or you can use the resort bus to get to AK or DHS. Similarly, on returning to the resort, you can grab either the bus to the Poly or the bus to the TTC which increases your chances of having a bus available when you need one. You're also within easy reach of the Grand Floridian and the Contemporary resort, so that it's easy to take advantage of their shops and restaurants as well. Other resorts are fairly convenient as well, because it's just a short hop to the MK to access a bus to any resort you wish to travel to, which really makes getting to ADR's fairly easy.
The Volcano Pool: It has a great slide, and a conveniently placed pool bar for beverages. It is near Capt. Cook's for snacks. And, in my mind, nothing beats sitting at the far end of the pool on the ledge with the water jets staring out across the lagoon at the castle and the water traffic.
The Cast Members: I find the CM's at the Polynesian to be some of the nicest and most helpful CM's on property. And, they all greet you with a warm "Aloha!".
The Longhouses: I know that some don't like this but, I love the way the resort is broken up into different longhouses. This makes it feel more like a resort to me. The walk between buildings isn't bad at all, and honestly, being out in the atmosphere of the resort really helps with the immersion. And, once in the buildings, the hallways are all straight, so there's no twisting and winding corridors to get lost in. The room size is also a plus. You definitely have a little more room to move around and don't feel cramped.
Restaurants: 'Ohana and the Kona Cafe are two of my favorite restaurants on property. I love being able to wake up and walk over to the Kona for breakfast and then hop on the monorail or out the front door to get our park day started. You're also within easy reach of the excellent restaurants at the GF and CR.
I'm admittedly a Polynesian fanboy, but I truly believe that the Poly holds a magic of it's own that Disney has just not been able to capture at the other resorts.