Top Anime

The unlabeled/leading series for each year are as follows:

    2000 - Banner of the Stars[2] (note that it has a 1999 prequel, Crest of the Stars[3] )
    2001 - Banner of the Stars II[4]
    2002 - Ghost in the Shell: Stand Alone Complex[5]
    2003 - Planetes[6]
    2004 - Monster[7]
    2005 - Aria the Animation[8]
    2006 - Kemonozume[9]
    2007 - Baccano[10]
    2008 - Kaiba[11]
    2009 - Eve no Jikan[12]
    2010 - The Tatami Galaxy[13]
    2011 - Hyouge Mono[14]
    2012 - Space Battleship Yamato 2199[15]
    2013 - Uchouten Kazoku[16]

While I would have made some slight changes (would have added shows like Sketchbook and Sora no Woto, removed shows like Moyashimon, Shiki, and Flag), the chart itself does a more than suitable job outlining the most notable anime televisions series over the past decade and a half.

To get an alternative perspective (after all, /a/ tends to look down on popular shows), I decided to go with MAL scores. While those scores are often poor measurements of just about anything, it's probably the best data set available without pulling APIs and running through weights. I decided to filter out every show based on the year they started to air and sort by score. It's worth noting that a few long-running shows may have made it past the filter. If anything, it's at best a measurement of how dedicated a show's fanbase is.
2013

    1 - [8.84] Monogatari SS[17]
    2 - [8.81] Attack on Titan/Shingeki no Kyojin[18]
    3 - [8.80] Kuroko no Basket 2nd Season[19]
    4 - [8.72] Hajime no Ippo: Rising[20]
    5 - [8.63] Magi: The Kingdom of Magic[21]
    6 - [8.63] Kingdom 2nd Season[22]
    7 - [8.63] Chihayafuru 2[23]
    8 - [8.49] Nagi no Asukara[24]
    9 - [8.48] The World God Only Knows: Goddesses Arc[25]
    0 - [8.44] Kill la Kill[26]

2012

    1 - [9.07] Gintama': Enchousen[27]
    2 - [8.79] Natsume Yuujinchou Shi[28]
    3 - [8.78] Fate/Zero 2nd Season[29]
    4 - [8.76] Bakuman. 3[30]
    5 - [8.64] Kuroko no Basket[31]
    6 - [8.58] JoJo's Bizarre Adventure (2012)[32]
    7 - [8.56] Psycho-Pass[33]
    8 - [8.51] Shinsekai yori/From the New World[34]
    9 - [8.51] Sakamichi no Apollon/Kids on the Slope[35]
    0 - [8.46] Sakurasou no Pet na Kanojo[36]

2011

    1 - [9.18] Steins;Gate[37]
    2 - [8.79] Gintama'[38]
    3 - [8.78] Hunter x Hunter (2011)[39]
    4 - [8.76] Ano Hi Mita Hana no Namae wo Bokutachi wa Mada Shiranai[40]
    5 - [8.64] Natsume Yuujinchou San[41]
    6 - [8.58] Mahou Shoujo Madoka★Magica[42]
    7 - [8.56] Usagi Drop[43]
    8 - [8.51] Fate/Zero[44]
    9 - [8.51] Bakuman. 2[45]
    0 - [8.50] Nichijou[46]

2010

    1 - [8.60] Rainbow: Nisha Rokubou no Shichinin[47]
    2 - [8.59] The Tatami Galaxy[48]
    3 - [8.55] Angel Beats![49]
    4 - [8.51] Katanagatari[50]
    5 - [8.50] Major 6th Season[51]
    6 - [8.50] Durarara!![52]
    7 - [8.44] Nodame Cantabile Finale[53]
    8 - [8.37] Bakuman.[54]
    9 - [8.35] Kaichou wa Maid-sama![55]
    0 - [8.31] Ookiku Furikabutte: Natsu no Taikai Hen/Big Windup! 2[56]

2009

    1 - [8.76] Hajime no Ippo: New Challenger[57]
    2 - [8.67] Zoku Natsume Yuujinchou[58]
    3 - [8.61] Major S5[59]
    4 - [8.60] Cross Game[60]
    5 - [8.47] Spice and Wolf II[61]
    6 - [8.46] Kemono no Souja Erin/The Beast Player Erin[62]
    7 - [8.44] InuYasha: Kanketsu-hen/InuYasha: The Final Act[63]
    8 - [8.43] Kimi ni Todoke[64]
    9 - [8.31] Phantom: Requiem for the Phantom[65]
    0 - [8.26] Tokyo Magnitude 8.0[66]

2008

    1 - [9.15] Clannad: After Story[67]
    2 - [9.00] Code Geass: Hangyaku no Lelouch R2[68]
    3 - [8.70] Aria the Origination[69]
    4 - [8.67] Toradora![70]
    5 - [8.54] Natsume Yuujinchou[71]
    6 - [8.45] One Outs[72]
    7 - [8.41] Junjou Romantica 2[73]
    8 - [8.41] xxxHOLiC Kei[74]
    9 - [8.39] Skip Beat![75]
    0 - [8.38] Major S4[76]

I'm too lazy to go any further.

Here are the shows that appear in both aforementioned lists:

    Chihayafuru 2[77]
    JoJo's Bizarre Adventure (2012)[78]
    Usagi Drop[79]
    Nichijou[80]
    The Tatami Galaxy[81]
    Katanagatari[82]
    Kemono no Souja Erin/The Beast Player Erin[83]
    Aria the Origination[84]