Code Geass. I watched it in 2008 and have rewatched it a couple times when I got older, and it still is my all time favorite. It has a perfect mixture of goofyness, cool battles, interesting character interactions, dramatic twists and has my favorite main character and ending of all time.
The early 00s were when I was probably the most engrossed in anime. As for my favorites from that era, I’d have to go with Cowboy Bebop and Outlaw Star. My female anime friends were obsessed with Inuyasha, which I could never quite get into, and my dudes were all about Trigun. Chrono Crusade was pretty great as well.