So here are the results! I actually wasn't familiar with a good number of the artists, but I think I did okay. :x
mujoyo,
famousalchemist,
arsenicgraffiti: I had to give up on yours otherwise I never would have gotten this finished. So, you WIN! :P Your prize is internet cookies.
I've put everything under a cut so I don't kill your friends pages.
harukakamiyacapsule
Aira Mitsuki - Colorful Tokyo Sounds NO.9Her music is pop-ish and happy without being over the top cutesy. She won some contest to be produced by an electronic artist.
Perfume - Computer DrivingProduced by Nakata from capsule, these three girls have a very fun sound that sounds somewhat teen pop.
COLTEMONNIKHA - Yum yum yummyThey sound much more like older capsule; they are mix of lounge and french pop, I think.
rankaMorning Musume
Mini Moni - Aiin! Dance no UtaThis kinda of reminds me of a Dance Dance Revolution song. It's really, really high energy and fun.
Matsuura Aya - Dokki doki! Love mailShe's probably a well-known classic at this point. This one of my favorites; it's not too super fast-paced but still has that cuteness to it.
garasu_no_barakokia
Rie fu - RoseHer stuff is generally more upbeat, but it's got a nice down-to-earth feeling to it.
Akino Arai - Hiru no TsukiHer stuff has the same kind of sort, mystic aura about it.
shizuka_bloomsYUI
Younha - Password 486She is a very talented singer-songwriter from Korea but she actually became famous in Japan first.
YUKI - StrawberryShe is from the old, hugely famous band Judy and Mary. Her voice may be hit and miss for some people; it's a little bit nasally and super-cutesy, but very unique.
ilinguistShing02
Epik High - Let It RainThey are a Korean group, but I think they have a pretty similar melodic rap sound, although their sound is a bit harder. One of my favorite groups by far.
Hideki Naganuma - Humming the BasslineHe composed many of the songs found on the Japanese Jet Set Radio soundtrack.
sers_sersMondo Grosso, Daishi Dance, Freetempo
Fantastic Plastic Machine - Don't You Know feat. Clazziquai ProjectHe has a very chill sound that mixes a lot of elements of lounge and harder electronic.
Jazztronik - Love TribeAs you can probably guess by the name, the music is very jazzy, but has club and/or hip-hop influences at times.
Towa Tei - MelodyI love TT. His music is very, very acid jazz and bluesy and just all around awesome.
glass_pyxMaaya Sakamoto
FictionJunction YUUKA - SeiyaI think her voice is maybe more similar to Ayumi's, but her style of music is very similar to Maaya's.
Akino Arai - VoicesShe is another classic anime theme singer; she has a very clear, bright voice.
silent_elementEri Nobuchika
SunMin - Koi no KisekiSunMin is actually Korean but sings totally in Japanese. Like Eri herself, she is way underrated!
Mika Nakashima - LIFEI think their voices sound very similar, especially on the ballads.
rehd_fawxSa Dingding
Unfortunately, I couldn't find anything super similar, but these two artists often include Chinese instrumentals, so maybe you'll like them.
JJ Lin - 不死之身 (Eternal Life)He's one of my favorite singers of all time, seriously. His songs, while he experiments with a lot of styles, tend to have some touch of traditional to them, I think.
Anson Hu - 願望 (Wish)Anson especially uses a lot of traditional sound, since he does themes for historical Chinese dramas. He tends to have much more upbeat songs.
kev193Base Ball Bear
Sparta Locals - PartyThey have a sort of indie punk feel to them but still manage to stay quite alternative at the same time.
DOPING PANDA - StairsAt times jazzy and chill, at other times fun and upbeat, this band is always an interesting listen.
Radwimps - YubikirikenmanVery similar to the hugely popular Mr.Children, they have a nice, down-to-earth acoustic sound.
appleminteAoyama Thelma
Crystal Kay - I Know(Half-)black woman power! Haha. I think CK's voice has a little more depth and power, but I think the two are definitely on the same plane.
Kato Miliyah - Last SummerShe has the same high, sweet tone, but her stuff is more pop.
cerulean18Under Graph
Fujifabric - KagerouThey have the same kind of chill indie thing going for them.
HY - Am11:00I think the male singer sounds pretty close to Under Graph's, and the female one is really awesome as well.
syunikissdKoda Kumi
Namie Amuro - TRY ME ~私を信じて~Unfortunately, I only have her older stuff which is mostly dance, but you can get a good listen to her voice in this one.
SOULHEAD - Got to LeaveWhile they are much less pop than Kumi, they are two of the top R&B/hip-hop female singers in Japan.
essouffleeMr.Children
remioromen - Himekuri calendarFun, unassuming, pop-rock.
BUMP OF CHICKEN - catch ballThey are another one of those classic Japanese rock groups.