The Runners-Up:

The way I rank anime can be boiled down to this code:

Great: I've watched and rewatched (at least the 'main, standout' section of the franchise, within two years of having watched it the first time so long as the there's a high quality subtitled bd/dvd/HD release for the second time available.  If it's unavailable, I can wait however long it takes until the release is available, because there's no point not watching a show in its final and perfect form for the conclusive time.  In addition, I don't have to rewatch Ghost in the Shell Movie 2 so long as I've rewatched the tv series.  Nor must I rewatch Macross 7 so long as I've rewatched Frontier, nor must I rewatch the Foxy Pirates section of One Piece so long as I've watched all the other arcs.  Watching the weaker portion of a franchise just once in full is plenty, there's no need to torture myself over sections of the story better left forgotten.), and is at least in the top 1/3 of mediocre and above series I've seen, and has left a strongly favorable impression as a 'must see anime' on me even after having rewatched it the second time.

Good:  I've watched in full.

Mediocre:  I've watched at least three episodes of the show but not all of them.

Bad:  I watched less than three episodes of the show.

Terrible:  I didn't even bother to watch a single episode.

Unranked shows I've watched twice, or in other words, the ones that got really close to reaching my rankings, might be a good window into how I make my selections.  In other words, these are the shows the top 175 went up against directly and beat:

Howl's Moving Castle
Iria: Zeiram the Animation
Ninja Scroll
Read or Die
REC
Tenjou Tenge
The Girl Who Leapt Through Time
X
Sora no Manimani
Kanokan
Moshidora
Akira
Noucome
Hell Girl

These are basically my 14 'runners-up' to my coveted ranked positions.  You could also call them 'motto Espada,' like in Bleach, in that virtually all of them used to appear in my rankings but were eventually kicked out by the intensified competition and my growth in taste as an anime connoisseur.

You really don't want to end up on this list.  It's a very depressing list of shattered hopes and dreams, like the silver medalist in the Olympics.  Or even worse, the guy who got fourth, that nobody cares about at all.

Just for completion's sake, I'll also jot down the 'good' series that I at least watched all the way through once, but didn't think was worthy of the title 'great' even after watching them all the way through.  These shows aren't really on par with the above list of 'motto espada.'  Perhaps they could just be called generic arrancar.  Like the ones Ishida and Sado were beating up on their journey through Hueco Mundo.  They're really strong compared to normal hollow, but in the end, that just doesn't mean much in the face of true power. . .

Ai Yori Aoishi
Asura Cryin'
Ayashi no Ceres
The Cat Returns
Chaos;Head
Devil Hunter Yohko
Dominion Tank Police
Dragon Half
Excel Saga
Fullmetal Alchemist Brotherhood
Furikuri
Futari Ecchi
Golden Boy
Guin Saga
Gunbuster
Mirai Nikki
I"s
Kamikaze Kaitou Jeanne
Kaze no Stigma
Kimikiss Pure Rouge
Laputa
Love Hina
Magic Knight Rayearth
Megami Kouhousei
Metropolis
My Neighbor Totoro
Nazca
Noein
Noir
Serial Experiments Lain
Shangri-la
Soul Link
The Law of Ueki
They Were Eleven
Trigun
Kannagi
Tytania
Vampire Hunter D
Vampire Knight
Vision of Escaflowne
Whisper of the Heart
Yoku Wokaru Gendai Mahou
Chrome Shelled Regios
Battle Angel Alita
Dual
Sora Kakuwo Shoujo
Blade of the Immortal
Tokyo Mewmew
Disgaea
Midori no Hibi
Girls Bravo
Rosario + Vampire
Sasamaki Koto
Ichigo 100%
Kiddy Grade/Kiddy Girl-And
Chu-bra
Omamori Himori
Ookami Kakushi
Hanamura Youchuein
Ladies vs. Butlers
Dance of the Vampire Bund
Needless
Koihime Musou
B Gata H Kei
Mayoi Neko Overrun
Busso Renkin
Ookami-san to Shichinen Notachi
Shiki
Asobi ni Iku Yo
Haibane Renmei
Higashi no Eden
True Tears
Seiken no Blacksmith
Nyan Koi
Yosuga no Sora
Fortune Arterial
Mai Hime/Mai Otome
Starship Operators
Sora wo Miageru Shoujo no Hitomi ni Utsuru Sekai
Dragon Crisis
Kore ha Zombie Desuka?
Fractale
Seto no Hanayome
Sengoku Otome
Hoshizora e Kakaru Hashi
Hidan no Aria
Oretachi ni Tsubasa wa Nai
Ga Rei Zero
Kimi to Boku
Astarotte's Toy
Saint Tail
Karigurashi no Arietty
Kanamemo
Guilty Crown
Shuffle
Ponyo on the Cliff by the Sea
Mashiroiro Symphony
Koe de Oshigoto
Thermae Romae
Yoake Mae yori Ruri-iro na
From Up on Poppy Hill
Kono Naka ni Hitori, Imouto ga Iru
Robotics;Notes
Mangirl
Tales from Earthsea
Photon
Ookami Kodomo no Ame to Yuki
Namiuchigiwa no Muromi-san
Koi to Senkyou to Chocolate
Garden of Words
Narawareta Gakuen
Watamote
Kodomo ni Jikan
Tayutama
Tsuki wa Higashi ni Hi wa Nishi ni: Operation Sanctuary
Tsuyokiss
Tsukuyomi Moon Phase
Okusama wa Joshikousei
W Wish
Final Approach
Maria Holic
Gakuen Alice
Sola
Prism Ark
Mangaka-san to Assistant-san to
The Wind Rises
Ushinawareta Mirai wo Motomete
Slow Step
Kanojo ga Flag o Oraretara 
Kimi ga Nozomu Eien 
Yahari Ore no Seishun Love Come wa Machigatteiru 
Elfen Lied 
Suisei no Gargantia 
Karin 
Nodame Cantibile 
Tsubasa Reservoir Chronicle
Accel World
Triangle Hearts
Chobits
They Are My Noble Masters
Sengoku Musou
Koufuku Graffiti
Juou Mujin no Fafnir 
Mouretsu Pirates 
Danmachi
Kaiji 
Charlotte
Ranpo Kitan
Wakaba Girl
Classroom Crisis
Rokka no Yuusha
Kuusen Madoshi Kouhousei no Kyoukan
Gakkou Gurashi 
Pretear 
When Marnie Was There

This is a very thorough list of all the possible competitors for the title of 'great.'  The 'great' series that did reach my rankings beat every single one of these shows, even though they were all worth watching until the end.  Mowing through this many foes is like when Ichigo and Ishida were having a hollow killing competition just for fun.  It makes you really appreciate just how strong the top 175 really are.  Even 175th is still high up on the totem pole, compared to all these others who didn't make the rankings.

These are all the missing pieces to my anime rankings puzzles.  All the data is now out on the table.  The great series, the nearly great series, the good series, everything that has any potential at all is laid out on the table.  If you like a show that isn't in my rankings or in this list, all I can say is you have rotten taste in anime.  If you've watched all 175 of my top anime rankings and still crave more, all I can say is consult this list of runners-up and let the good times roll!