Title pretty much says it all, from the year 2000 up to 2009, what are the ones that people will be bickering about, for better or worse, in the coming years? Yes, I'm talking about the shows and series that will go down in the annals of the industry.
Of course opinions may vary, what made an impact in the US may or may not have made an impact in let's say Argentina, Philippines, Iraq, or even Japan. But please, have some factually sound basis for your opinions. You just can't mention something out of nowhere. Remember, your favorite anime doesn't necessarily mean it's definitive.
And of course, we're all free to mention a series here, for BETTER or WORSE. I guess that means anyone could say something like "Bleach is a defining anime, people will remember it for being utterly pathetic", so do not whine when somebody mentions your show with a negative note.
Okay here's a few:
TTGL - Perhaps one of the most definitve mecha titles of this decade to grace our screens. Best remembered for its over-the-top testosterone-fueled action and the largest mecha ever.
Monster - Meticulously done, Monster is a critical favorite. Though it may not have that much popularity (as compared to some other titles like Naruto or FMA) to boast, it's a widely considered masterpiece.
Naruto - Love it or hate it, it amassed a great deal of fans, brought a newfound popularity and definition to the word "ninja", and made people more critical towards fillers.
P.S. but of course, in some cases, some titles may not be definitive right now but would likely to create more impact in the future.