Entering into the Top 10, here is #10 to #6...
10. Gurren Lagann
Format: TV (27 episodes)
Debut: April 1, 2007
End: September 30, 2007
Website: Japanese, English
Previous Spot: #10
GAINAX produced its biggest hit since (#14) FLCL in Gurren Lagann, a runaway sleeper in 2007. A slickly animated mixture of giant robot action, shounen elements, comedy, and epic drama, it has grown a large base of fans and critical praise, a good portion of which is extended to its masterful, eclectic score and impressive production values. An expanding number have gone as far as to consider it a “redefinition” of the its genre—much in the same vein as the studio’s earlier Neon Genesis Evangelion (the best of the previous decade).
Personal Note: Prior to G-L’s success, GAINAX had been a relative rut in terms of good original stories. After (# 14) FLCL finished, the studio had not created an anime that had resonated as well as that series had. Magical Shopping Arcade Abenobashi (worked on by much of G-L’s staff, which also served as a bit of a breeding ground for that show’s concept) and Mahoromatic had good praise and fanfare, though not at the level of the aforementioned OVA or some of their past popular shows. On the other end of the spectrum, He is My Master and a few other works didn’t get too much of a response, while their 20th anniversary project, This Ugly and Beautiful World, had its fans but was generally derided. Re: Cutie Honey, a co-feature tie-in with Toei Animation to the live-action movie from Evangelion and Gunbuster creator/director Hideki Anno (who also helmed the anime), was a notable title, but not a big time hit nor an original adaptation. Their most prolific work, Aim for the Top 2! Diebuster [Gunbuster 2] (by (#14) FLCL’s director, and Anno’s protégé, Tsurumaki) was more well-received and won a few awards, though it too was based off of a pre-existing. G-L broke that drought and saw GAINAX return to form, showing that the studio still had it left in them.
While I won’t go as far to call it a “genre changer” (more close to being a “reimagining” of sorts), I do think that is a masterpiece across any genre—a sentiment has followed through with others with its stateside release and television broadcast. Much like (#11) Gungrave, it could have been horribly mediocre given the material, yet instead, it was carefully constructed and handled, resulting in a solid and well-done work. And like with seemingly all of GAINAX’s hits, production wasn’t always smooth. A poorly made Episode Four and staff sniping at a more popular, competing show created much controversy, resulting in a PR disaster and the resignation of one of the show’s producers and studio’s founder, who made disparaging remarks at the more vocal, critical fans on the Internet. In spite of this, the end results of their labor created a show that has managed to even rival GaoGaiGar: King of Braves as the best super robot show ever made.
9. Eureka Seven
Format: TV (50 episodes)
Debut: April 17, 2005
End: April 2, 2006
Website: Japanese, English
Previous Spot: #9
Eureka Seven has been one of the most well-reviewed series thus far and has been considered among the best from relative newcomer BONES. A delicately paced drama complimented by high production values (for a fifty episode series) and intense sky-surfing mecha (!) action, it is also one accentuated by its large cast of characters, award-winning designs, and varied concepts and messages.
Personal Note: E7 is one of a number of high-caliber shows from BONES, a Sunrise off-shoot formed from the success of Cowboy Bebop, which has only been in existence since late 1998. While not one of the studio’s biggest hits initially (its pacing, eccentricities, and cast having been sources of complaints from some), it does have a decent following and many glowing reviews. These have come notably as the series progressed, as its story weaves together many of the elements shown earlier and builds upon them. E7 is a prime example of solid storytelling at its best and remains one of the most underrated shows (when compared to others and their popularity) in anime. However, it appears that it is slowly, but steadily, gaining more recognition and favor.
8. Millennium Actress
Debut: January 23, 2001
Previous Spot: #8
One of the most widely celebrated anime films of this or any decade, Millennium Actress is also considered to be the best from master director Satoshi Kon. Much of its accolades have been extended to its production and wonderful, human story.
Personal Note: While I’m not exactly a big fan of Satoshi Kon’s work, MA has been a film of his that I have long wished to see. Prior to Spirited Away, which came out later in the year, it gained a great deal of positive reception and was regarded as the best of the young decade. Though the more popular Hayao Miyazaki feature has taken its spotlight, whenever Millennium Actress is mentioned, nothing but high praises continue to greet it.
7. Gankutsuou: The Count of Monte Cristo
Format: TV (24 episodes)
Debut: October 5, 2004
End: March 29, 2005
Website: Japanese, English  
Previous Spot: #7
GONZO’s most critically-acclaimed work, Gankutsuou, a futuristic adaptation of the Alexandre Dumas classic, The Count of Monte Cristo, was one of the most radically-visual animated series in recent memory and one of the best shows, as well, with its compelling drama, score, characters.
Personal Note: Gankutsuou was a major achievement for GONZO, as it showed that the studio was capable of producing more than one or two great, roundly well-received show ((#12) Last Exile, SaiKano). Its artistic style, which was the signature aspect of the series, would later be emulated in 2006’s Red Garden and its success would later fuel the studio’s adaptation of William Shakespeare’s ubiquitous Romeo & Juliet (under the title of “Romeo x Juliet”) in 2007.
Format: TV (26 episodes)
Debut: January 21, 2002
End: September 10, 2002
Previous Spot: #3
One of BONES’ earliest productions, RahXephon gained immediate notoriety due to its similarities to the classic Neon Genesis Evangelion. However, that consensus changed afterwards, as many now regard it as being a superior work. Even without the comparisons, the series has been widely regarded as one of the best ever made. Its impressive animation quality and a great score accentuate its excellent story.
Personal Note: When I first made this list, I was quite conflicted about RahXephon’s No. 3 spot on the list. While I did hold it in a very favorable light and it had enough credibility in meeting the criteria to justify its placement, I had wondered if I had placed it too high, perhaps due to my esteem of the series. Having ran it through my mind over the course of the year, and more so recently, I've decided to reduce its seating on the list to #6, as the show has not had nearly as big an impact as the others above it nor has it received as widespread an accolade as them. Certainly, it would be great to see it higher, but it was only fair in reassessing its standings given the circumstances. RahXephon, like (#11) Gungrave, is one of my favorite anime, so I had taken extra precaution in placing it among the best of the decade (...so far), out of respect of keeping this unbiased.
That being said, there were three things that were going for this: the number of people who have considered it among the best, the actual critical merits of the show, and the number of people who have claimed that it was superior to Evangelion, often called “the greatest anime ever made.” All of those rank high, even though I disagree with some of what is said. The Evangelion comparisons are warranted, but I don’t necessarily think that one is better than the other in that sense, as they have their own merits and are ultimately different series with different purposes. It wasn’t something that figured very highly into its placement, as it didn’t necessary denote that RahXephon itself was the “greatest”, but it was a consideration, nonetheless. That aside, I have regarded it as being better overall, and critically, I have been hard-pressed to find many, if any, flaws in it. It is very deserving of being one of the Decade’s Best, and one of the best anime ever made (...not bad for first-time director Yutaka Izubuchi, a long-time designer). Just consider its new spot as an “inflation adjustment”...