Unlike the G-films in the Showa and Heisei Series, most of the films that appear in the Millenium Series do not follow one consistent timeline, and all but two films in the series take place in an entirely different alternate reality, with a completely different version of Godzilla, whose history, and sometimes even his very nature, is unique and distinct from the Godzilla appearing in every other film in this (or the previous two) series, and the events in one film will have no relation to the events in each subsequent entry...with two notable exceptions.
First, the initial G-film, Godzilla, King of the Monsters (1954), which was not part of the Showa Series alone, but was the launching point of not only the consistent timelines seen in both the Showa and Heisei Series, but also every single film that appears in the Millennium Series. Thus, in each movie in this G-film series, the basic sequence of events seen in the first G-film, specifically Godzilla's 1954 attack on Tokyo, are part of the official canon of each film in the third series.
Also, please keep in mind that certain specific events seen in the first film may not have occurred to the letter in each Millennium Series G-film, an example being Godzilla vs. Megaguirus (2000), where Godzilla's 1954 attack on Tokyo did indeed occur precisely as seen in the first G-film, but his disintegration by the Oxygen Destroyer at the very end of the movie didn't occur in that particular reality, as Godzilla simply disappeared back into the depths of the Pacific Ocean without being temporarily destroyed by Dr. Serizawa's deadly device. However, in Godzilla Against Mechagodzilla (2002), Godzilla was indeed still nullified by the Oxygen Destroyer, though his skeleton remained intact, a very important plot point for this and the subsequent sequel (see below).
Secondly, it appeared that the first three films in this G-series were intended to be "showcase" movies, with Toho looking at each take on the Big G for the purpose of eventually shifting the Millennium Series to a single, consistant timeline by the fourth movie in the series. This was done with Godzilla Against Mechagodzilla (2002), which established a consistant timeline, and this continuity continued into the next film in the series, Godzilla: Tokyo S.O.S. (2003).
However, by the time the fifth film in the series was released, it was evident to Toho that the Millennium Series was in serious financial difficulties. Due to an insistance on maintaining its basic protocol in regards to producing the G-films, Toho realized that the series was faltering as badly as the Showa Series three decades earlier, and decided it would no longer be profitable to continue the production of G-films.
Nevertheless, since 2004 was going to be Godzilla's 50th anniversary, Toho decided to scrap the consistant timeline it had established with the last two movies and return to the alternate reality format for one exceptionally budgeted farewell film, Godzilla: Final Wars, in the hope of bringing the third G-series to an end with some style, and hopefully some money for the company.
Following the 50th anniversary swan song production, Toho announced that it would cease producing G-films for the forseeable future, stating that it would be at least ten years, if ever, before Toho would consider producing another G-film.
Thus ends the third G-series and thus begins the third "in between" period for the Sacred Beast of the Apocalypse, the future beckoning to G-fans with an intensity as powerful as one of the Big G's atomic beams.
GODZILLA MILLENNIUM ERA FILM SERIES
Godzilla 2000 (1999)
Godzilla vs. Megaguirus (2000)
Godzilla, Mothra and King Ghidorah: Giant Monsters All-Out Attack (2001)
Godzilla Against Mechagodzilla (2002)
Godzilla: Tokyo S.O.S. (2003)
Godzilla: Final Wars (2004)