1997 - Revolutionary Girl Utena. Arthouse feminist show by one of the directors of Sailor Moon. Also has a movie.

1998 - Cowboy Bebop. Atmospheric classic inspired by western cinema and beloved in the west to this day.

1998 - Initial D First Stage. Exciting racing show with an incredible soundtrack. Season 1 might have the worst CGI, but that's also where the show peaks, as the following seasons have a worsening pacing and side characters get pushed out of the frame completely by the dreadful Season 5.

1998 - Serial Experiments Lain. You've probably heard of this one.

1999 - Turn A Gundam. Yoshiyuki Tomino's late career classic.

1999 - [CW] Great Teacher Onizuka. This is a show of contrasts. Where it's good, it's really good. Where it's bad, it's really bad and uncomfortable. It is however absolutely a show that was considered a classic for many years. One of the characters is treated in a very ableistic way unfortunately.

1999 - The Big O. Again inspired by western media, it was a huge flop in Japan - but as a mecha show it does what it does really well.

2002 - Azumanga Daioh. The first slice of life/random nonsense go show, and at the same time the best at it - rivaled only by the more absurdist approach of Nichijou.

2006 - Welcome to the NHK. A show about social isolation, being preyed upon by capitalism and mental health issues. Has some flaws, but is absolutely worth watching.

2007 - Kaiji, Ultimate Survivor. A gambling drama that is highly likely hook you really hard, sprinkled with anti-capitalism on top and Nobuyuki Fukumoto's unique signature artstyle.

2009 - K-On! The platonic ideal of the pure slice of life show. IMO it only gets good in season 2.

2011 - Nichijou. As mentioned before, a more surreal Azumanga Daioh, with quality animation by the workers of the renowned Kyoto Animation.

2012 - Jojo's Bizzarre Adventures. Similarly to Breaking Bad, it lives up to the hype.