I've decided to list not only the sets I've fully completed, but also the sets that are near complete as well (only missing a few cards to finish).
Ayashi no Ceres
9 SP
9 Washi
62 Regs
1 Promo
Bleach CM1
9 SP
72 Regs
Bleach CM2
9 SP
72 Regs
Bleach CM3
9 SP
72 Regs
Cardcaptor Sakura ~ Sakura Card Chapter
27 Rare
89 Regs
1 SP
Binder
Binder Card
Cardcaptor Sakura Trading Collection 2
27 SP
45 Regs
Chobits Kadokawa (Need Promo B9, B10, E37)
2 SP
7 A
8 B
7 C
36 D
36 E
Binder
Clamp Gold Cards
16 Gold Cards Illustrated by Clamp
DN Angel Kadokawa
2 Clear C.SP
6 Color Metallic CM.SP
6 Silver Metallic SM.SP
86 Regs
1 Box B.SP01
1 Asuka Promo Card
Flame of Recca TC
9 SP
45 Regs
Full Metal Alchemist CM1
9 SP
72 Regs
1 Roy Mailaway
Full Metal Alchemist CM2
3 AR
9 SP
90 Regs
Full Metal Alchemist CM3
4 AR
9 SP
90 Regs
1 Animedia Promo Card
Full Metal Alchemist CM4
4 AR
9 SP
90 Regs
Full Metal Alchemist CM5
18 SP
54 Regs
Fushigi Yuugi PC1
9 SP
72 Regs
2 Box Cards
Fushigi Yuugi Shichiseishi Character Collection (for what's been released so far)
8 Suzaku
8 Seiryuu
9 Genbu
3 Byakko Mailaway
5 Drama CD Inserts
Mailaway Binder
Hikaru no Go TCG Premium 1
5 TCG Cards
Hunter X Hunter CM1 Special
2 SP
18 Regs
Inuyasha CM2
4 SP
7 EX
63 Regs
Inuyasha CM3
3 SP
90 Regs
Inuyasha World Hobby Fair
4 SP (All Manga Images)
Inuyasha Bromide 1
8 SP
36 Regs
Ouran Koukou Host Club
18 SP
54 Regs
6/8 Promo
1 Mailaway
Rurouni Kenshin Senkou no Maki TV
9 Cards
Slayers Comic Images
6 SP
72 Regs
Tsubasa Chronicle Trading Collection
18 SP
45 Regs
Tsubasa Chronicle Memorial Carddass
14 Rares
49 Regs
Tsubasa Chronicle Amada Gum Collection
18 SP
45 Regs
Tsubasa Chronicle Clear Cards
4 Clear Cards
X Kadokawa Shoten
72 Regs
18 Specials
1 Binder Card 00
1 Box 0
6 X Promo
Binder
X Kadokawa Limited Edition
27 Limited Edition Cards
XxxHolic Clear Cards
3 Clear Cards
Yu Yu Hakusho PC2
9 SP
18 Rares
99 Regs
3 Box
1 Mailaway
Ah! My Goddess M2 Screenplay Version
80/81 Regs
22/36 SP
5/9 Tribute
6/9 Cel
5/9 Laser
6/9 Seal Puzzle
Black Cat
17/18 SP
45 Regs
2 Box
1 Promo
1/5 AG
Bleach CM4
15/18 SP
54 Regs
Cardcaptor Sakura CM4
5 SP
179/180 Regs
Cardcaptor Sakura ~ Clow Chapter
26/27 Rares
89 Regs
1 SP
Binder Card
Binder
3 Inserts
Cardcaptor Sakura Trading Collection 1
15/18 SP
45 Regs
Fate/Stay Night Fate Fact Silverblitz
5/9 SP
99 Regular
1 Mailaway Binder (Getting this)
Fate/Stay Night Movic 1
8/9 SP (Getting 3 missing SPs.. may take a while tho)
56 Regs
1/4 Box
1 Mailaway
Fruits Basket
54 Regs
3 Box
Full Metal Alchemist Bromide 1
6/9 SP
26/36 Regs
Full Metal Alchemist Gangan vs Neo
1/2 Energy
6/9 Leader
48/57 Character
15 Item
10 Break Event
3 SP
1 Card File
Fushigi Yuugi Perfect Collection 2
5/9 SP
62/63 Regs
1/3 Box
Inuyasha CM1
3 SP
6 EX
62/63 Regs
Inuyasha Japanese Gaming Set 4 (Missing 1 Rare)
xx Rares
xx Regs
Inuyasha Bromide 3
6/9 SP
36 Regs
Kyou Kara Maou! Part 4
5/9 SP
52/54 Regs
2/3 Box (Getting Box 3)
1 Promo
1 Mailaway
Kyou Kara Maou! Carnival Edition
6/9 SP
54 Regs
1/3 Box
2 Box Inserts
Magic Knight Rayearth OVA
8/9 SP (Getting SP1)
60/90 Regs
1 Box (Getting the Box card)
1 Mailaway Promo (Getting it!!)
1 Atari Card (Woohoo!!)
Matentai Loki Ragnarok
2/6 SP
12/18 Rare
54 Regs
1/3 Box
Porter Sa Croix (Azumi Tohru)
2/3 SSP
5/6 SP
72 Regs
1/4 Promo
Prince of Tennis Shining Clear 1
3/9 SP
10/18 Rare
65/72 Regs
Prince of Tennis Shining Clear 3
5/9 SP
11/18 Rare
72 Regs
Prince of Tennis Shining Clear 4
5/9 SP
11/18 Rare
45 Regs
Prince of Tennis Special Bromides 2 Summer
1/3 Rare
14/18 Regs
Rurouni Kenshin Emakizoushi
7/9 SP
90 Regs
1/2 Box
Shakugan no SHANA
15/18 SP
63 Regs
PR01a/b
Slayers Next Perfect Collection
121/122 Regs
4 Clear SP
Slayers Try Perfect Collection
5/6 Character SP
3 Checklist SP
171 Regs
Spiral Movic
4/9 SP
9 Rare
53/54 Regs
2 Promo
Yu Yu Hakusho PC1
8/9 SP (Getting 2 SPs)
26/27 Rare
108 Regs
4 Box
1 Mailaway
Binder