A few things already listed in more detail:
1) Pokemon cries - Generally they're just awesome. My wife is starting to get annoyed because I keep pointing out how awesome Staraptor sounds every single time I throw him out.
2) Poketch - Ok, it could have been a LOT better overall, but its still pretty useful. The item finder alone is worth the screen space, and marks the first time in the series I've ever used the thing. The new item finder is simply fun, useful, and non-intrusive, making hidden items a major part of my exploring.
3) Battle animations. On the whole, they look great. Say what you will about Roar of Time's usefulness (ie not much) but the first time Dialga used it against me, I had a whole new sense of what it would be like to battle a "legendary" Pokemon.
4) Day/Night cycle - Not only is it back, but the Pokedex lets you change the time in the area found section so you know when to search as well. Night is also WAY brighter than it was in GSC, which was the sole reason I was glad to see it gone in RS. In GSC I simply couldn't see at night (which is when I play the most unfortunately), but in D/P its greatly improved.
5) Story - while it doesn't feel as complete as Emerald's clash of the trio scene (it has the same pulled apart feel that Ruby/Sapphire suffered from, hopefully the 3rd game will change things), the way its told is simply more compelling and mature than any other Pokemon game. The legendary trio fit in to things far better than before and the existence of Dialga/Palkia blend into the story far earlier, making it less of a side story than the Team Aqua/Magma scenes of RS.
The supporting characters are also the strongest ever, with both rivals showing significant personalities (your main rival moreso than Rowan's gopher). Your main rival essential accomplishes the role Wally was supposed to fill in RS by blending the best aspects of Gary while maintaining his own unique quirks. Team Galaxy in general fits into the world better than the teams that came before it, and Cypher's motives are well explained and followed through. I also have to give this story props as the first time I've felt justified catching the Legends and making them a part of my team.
6) New Pokemon - In general, the new Pokemon are great. Lots of great new designs and unique abilities, stats, and mechanics. Honestly, most of them aren't really my style, but they definitely fit in well with other people's teams and fill up missing concepts for my friends. The fact so many old Pokemon got bumped up with new evolutions means that fewer people will be dumping their favorite evolution lines for something better and can really show off their favorites. In particular, this gen really helped a lot of the black sheeps from GSC find a place in the 500-600 stat range that seems to be the essence of competetive Pokemon.
7) Game Design - This is simply the best designed game as far as progress and flow are concerned. While encounters seem to be up, it seems much easier to keep out of the grass when you don't want to battle. Fewer mass expanses of ocean really help make traveling more enjoyable as well. The route layout is fantastic, mostly because it's really large and expansive, yet its looping nature removes a lot of the logic gaps that were always popping up in previous games. There's less "I've magically arrived before you!" encounters with your rivals and I can usually logically trace their location between meetings without wondering why I didn't run across them somewhere between.
Of course, special mention needs to be made to the Pokedex. Not only do we have a system that reinforces the "gotta catch'em all" mechanic that made Pokemon such a compelling experience in the first place, but its done in a way that makes the system less frustrating despite the 493 species to catalog. The strategic placing of rare Pokemon in NPC trainers ensures that you'll naturally accomplish the National Dex, but simultaniously encourages seeking out battles and checking optional dungeons thoroughly. Also, pushing a large portion of the new Pokemon into the post Elite 4 game helps encourage the concept that Pokemon is a persistant world, that only begins once you've defeated the "last boss".
8) WiFi - Probably the greatest system introduced in D/P, the ability to communicate with people all over the world is a huge leap forward. GTS has its faults, but generally works out well. Friend codes fill in the gaps and patch up the faults pretty well with the help of a solid message board community. I'm looking forward to the random battles in PBR, and while I'd rather have them now, I'm glad Nintendo limited them to one side or the other. I'd hate to find a lack of opponents because Nintendo split the random battle community over two games that cannot properly communicate with each other. In any case, WiFi finally gives Pokemon the communication structure its longed for since the days of RBY, and is probably the strongest case for calling this the best Pokemon generation ever.
