Now that I'm home from work and not typing on a cellphone, let me expand upon why I love the first three Millennium films.
Godzilla 2000 is one of the first Godzilla films I owned on VHS. Until I was seven or eight and had my first G-Fest, it was just that one, KOTM, Godzilla vs. the Thing, Ghidrah, Revenge, Battle For Earth and Space Godzilla, plus Gamera: Guardian of the Universe. I used to watch it religiously and for a time it was my favorite Godzilla film, until I discovered Hedorah. Even leaving nostalgia out of the mix, I maintain that Godzilla 2000 is stronger than any of the Heisei films and I greatly enjoy most aspects of the film.
For starters, I think the characters are some of the best of any Godzilla film. The relationship between Shinoda and Io is one I enjoy. I'm a sucker for father-daughter relationships, and I think theirs was developed well. The rivalrous relationship between Shinoda and Katagiri, with Miyasaka caught in the middle, is an interesting one, too. I think Katagiri is one of the better villains of the franchise; unlike the gleefully evil bad guys of the Showa era, he's a believable villain: a bureaucrat with noble intentions but ruthless methods and a few screws loose.
Another thing I like in Godzilla 2000 is that it actually has scenes where the human characters are endangered by the kaiju. Seriously, given how many Godzilla movies there are, it's amazing how few actually show their protagonists being directly menaced by Godzilla and company. The scene where Godzilla pursues Shinoda's SUV through the tunnel is effectively thrilling and, while a bit overacted, Katagiri's demise at Godzilla's hand is a memorable scene as well.
Moving onto Godzilla himself, I love the MireGoji design. I think the suit is usually pretty convincing and the jagged purple spines add some nice flare to the character. I also feel that G2K captures Godzilla's anti-heroic portrayal better than a lot of films do. As for Godzilla's adversary, the Millennian UFO is an interesting new take on the alien invasion story. Instead of a race of aliens who look like people in goofy get-ups, it's a mysterious, amorphous being that needs to use another's DNA just to survive on Earth. That's cool, fresh take; just a little better than space apes and cockroaches.
Let's move onto Godzilla vs. Megaguirus, the one I'm sure no one else will say anything positive about. I should really just copy and paste what I already said in this film's thread, but the movie needs more love so I'll reiterate briefly. While the execution is far from perfect, from a conceptual standpoint I feel that Megaguirus is the most interesting Godzilla film since 1989. We've got giant prehistoric bugs, black hole guns, a flooded Tokyo and a revenge-driven heroine in the mix. That's a low of fun new ideas for a franchise whose "Big Nuclear Dinosaur Fights Other Big Ugly Thing" formula had started to grow annoyingly repetitive.
Megaguirus is one of my favorite kaiju. After Biollante, she's my favorite post-Showa kaiju without a doubt. Her design is pretty awesome, my personal favorite of all Toho's insect kaiju (though Legion tops her in this category). She exhibits a cruel and cunning personality during her battle with Godzilla and that battle... damn. I can say without a doubt that it's my favorite kaiju fight of the whole series. When I bought a bootleg DVD at my first G-Fest, I didn't much care for the movie but I would watch this battle over and over again. After all of the sparky, sluggish body slams and notorious beam wars of the Heisei series, and the rather pedestrian climactic fight in G2K, we get a contest of strength and speed that's a lot of fun to watch. We see Godzilla adapting to his enemy's strategy in order to overwhelm her, which is cool. Often these fights just go on and on until one monster gets chicken or pulls out some deus ex machina attack (looking at you, Godzilla vs. Mechagodzilla '74).
And now for the big one: GMK. I could gush about this one for hours. It's probably my favorite Godzilla movie, and without any doubt my favorite since 1975. The characters are well-written and likable and, as in G2K, they're effectively placed in the middle of the kaiju's battles to create suspense. The effects work is possibly the zenith of the whole franchise (excluding Ghidorah's transformation scene, which looks frustratingly fake thanks to the bad glowy CG work). The music is downright epic; I have more tracks from GMK on my Godzilla playlist than any other film. The action scenes are well-constructed and paced; never do they end too quickly or overstay their welcome. I also find this one of the more thematically interesting Godzilla films. The idea that Godzilla is a product of Japan's negligence in remembering the atrocities committed both by and against the nation people during WWII is a fascinating one, and a cool new take on the character.
Finally, let's give a shoutout to Baragon. I always like the little guy, but this movie made me love him. His one-sided fight with Godzilla is one of the better kaiju battles in the series, and stands as proof that Godzilla's opponent doesn't need to be strong to give him a great battle.
The first three Millennium films, and especially GMK, are among the Godzilla films I hold in the highest regards. While I almost never revisit the Heisei films, I still pull out all three of these at least once a year. Obviously, all have their flaws, but I see a lot more positives than negatives, even in the much-maligned Megaguirus.