Can you recall all or most of the anime you've watched completely?  

Well, here is the list
Ice Age
Ice Age 2
Alladin
Hanuman
Ants

and many more

I have watched so much that I've lost count. But I do have a profile at myanimelist that helps me keep track of what I've seen and read. The only downside is that I havent' updated there in a while. Off the top of my head, I've completed the following series:
Rurouni Kenshin, Samurai Champloo, Peacemaker, Samurai Deeper Kyo
Midori no Hibi, Vision of Escaflowne, Full Metal Panic
Full Metal Panic Fumoffu, Full Metal Panic: The Second Raid
Zeta Gundam, G Gundam, Wing Gundam, Gundam Seed, Zombie Loan
Gundam Seed Destiny, 08th MS Team, Infinite Ryvius, Ninja Scroll
El Hazard, Fruits Basket, Soul Hunter, Arc the Lad, Nadesico
12 Kingdom, Outlaw Star, Dear Boys (Hoop Days), Gilgamesh
Whistle!, Eyeshield 21, Hikaru no Go, Ookiku Furikabutte
Slam Dunk, Prince of Tennis, GTO, Gokusen, Shura no Toki
Blue Seed, Loveless, Fullmetal Alchemist, Ayatsuri Sakon, Slayers
Slayers Next, Slayers Try, Trigun, Tenchi Muyo, Tenchi Universe
Shakugan no Shana, The Third, Trinity Blood, Utawarerumono
Seirei no Moribito, Vandread, Vandread 2nd Stage, Initial D
Initial D 2nd Stage, Initial D 4th Stage, Weiss Kruez
Hungry Heart, Hunter x Hunter, Yakitate!! Japan...

I think that's a long enough list. And that's just for the series. I've also seen a bunch of movies and OVAs too.

I can mostly recall...I haven't watch Piano no Mori yet. Since it's highly recommended, I will watch it. As for me, I will highly recommend Toki wo Kakeru Shojo (The Girl who Leapt through Time). It's my favorite Anime Movie.

I use myanimelist.net to keep track of the anime I've watched, watching, dropped and etc.

You can check it out here: http://myanimelist.net/profile/chan-chan

or my blog: http://chan-chan-anime-blog.blogspot.com/

Wow, a nice list there. I believe I've already lost count. ^^ But I remember the ones that I really liked in details, like Samurai X, Fate Stay Night, Hikaru no Go; Sometimes I hope that I can forget everything about it so I can watch it again for a second experience. ^^

now this is a tough one, lets me list 1) sailormoon 2) Tnde burring 3) chibi maruko 5) one piece 6) samurai X 7) slamdunk 8) ayashino ceres 9) darker descendent 10] rave master 11] detective conan 12] jigoku shojou seasone 1 and 2 , now three 13] ouran high school 14] ranma half 15] apple seed 16] Beck , mongolian chop squad 17] yamato nadeshiko shici henge 18] darker than balck 19] black jack 20] moyashimon 21] big wind up or so called ookiku fuributte 22] paradise kiss 23] Great teacher onizuka 24] cromatie high school 25] school rumble 26] naurto the first one not shippuden , i didnt watch shippuden 27] death note anime 28] bleach 29] eye shield 30] keroro 31] honey and clover 32] ah! my goddess 33] god! save the king 34] tactics 35] doreamon 36] gundam seed destiny 37] dragin ball GT 38] muka muka paradies 39] fullmetal alchemist and the movie something shambala 40] alice academy 41] gravitation 42] xXxholic 43] inuyasha 44] la corda prima passo 45] hellsing 46] ayakashi japanese horror 47] air gear 48] shaman king 49 ] kyo samurai deeper 50] friut basket 51] love hina 52] initail D all the stages :)
Thats all i can remember for now.. cant remember much .. :)

hmmmm....

it just only few that i can recall
fushigi yuugi
ghost fighter
card captor sakura
samurai x
astro boy
zoid
zoids genesis
gakuen alice
mai-hime
naruto
bleach
sailor moon season 1,2,3
pokeman season 1,2
flame of recca
slum dunk
shakugan nu shana
tenjo tenge
one piece
naruto shipuden
dragonball z and gt
azumanga daoih
black blood brother
cayote ragtime show
fruit basket
mirmo season 1,2
mojacko
doraemon
law of yuweki
love hina
yamato nadeshiko
lupin III
bakugan brawlers
mushiking

there are more but i never recall it. it's been along years to recall them all

it is SO hard to remember..
the ones i remember are NANA, Death Note, Pretear, are the ones i can remember..>.<

I love to watch anime and I could say I watched a lot of them completely,some of them are:Inuyasha,Vampire Knight,Dn angel,Ai no kusabi,Yuyu hakusho,Kaleido star,Yugioh,Okane ga nai,Gravitation,Saiunkoku monogatari,Tokyo mew mew,Shaman king,Death note,Full metal panic,Full metal alchemist,Blood +,Rg veda,Magic knight rayearth,Vampire princess Miyu,Peacemaker kurogane,Angel feather,all Inuyasha movies.And of course Bleach and Naruto but are still ongoing!