International shipping:

These are the main clothing brands that ship internationally. 

Alice Fururun (second hand)
Angelic Pretty (sweet)
Angelic Pretty USA (sweet)
Anna House (sweet, cheap, custom)
Antique beasT (gothic, ero)
Atelier p-i-n-k-y (punk, gothic)
Baby the Stars Shine Bright/Alice and the Pirates (sweet, gothic, pirate, menswear)
Blasphemina’s Closet (classic, custom)
Bodyline (sweet, gothic, punk, cheap)
Candy Violet (sweet, classic, casual)
CD Japan (Moitie, Maxicimam, Lumiebre, Deorart, Listen Flavor, Sexpot ReVeNGe)
Chantilly (classic, gothic)
Clobba Online (taobao brands, custom)
Closet Child (second hand)
Clothing Drop (second hand)
Cute Parade (sweet)
Elegy (sweet, boystyle)
English Charm (classic, gothic)
Ergi (classic, gothic, pirate, steampunk, menswear)
Fanplusfriend (gothic, classic, sweet, punk, menswear, custom)
h.Naoto (punk, gothic, menswear)
Haenuli (sweet, classic)
Harajuku Hearts (Algonquins, Atelier Pierrot, Deorart, Listen Flavor, Maxicimam, Metamorphose, Putumayo, Sexpot ReVeNGe)
Il Sangue
Innocent World (classic, sweet)
JIMU (second hand)
Juliette et Justine (classic)
Lady Sloth (classic)
Lily of the Valley (sweet)
Lusty’n Wonderland (classic)
Marguerite in Strawberry Skies (sweet)
Mary Magdalene (classic)
Metamorphose temps de fille (sweet, gothic)
Mfashion (Innocent World, Maxicimam, AP, Metamorphose, BTSSB, Bodyline, Heart E, Victorian Maiden etc)
Miho Matsuda (classic, gothic, casual)
Milky Ange (classic)
Neo Tokyo (AP, Chocomint, Deorart, h.NAOTO, Marble, Princess Doll, Sexpot ReVeNGe)
One Day in Paradise (BTSSB, h.NAOTO, Putumayo, Anna House, Fanplusfriend, Metamorphose, Taobao brands)
Porcelain Doll (sweet)
Qutieland (Taobao brands)
Schwarz Schmetterling (classic)
Sweet Rococo (custom, design it yourself) 
Tokyo Rebel (BTSSB/AatP, Innocent World, Putumayo, Sexpot ReVeNGe, Atelier Pierrot, Victorian Maiden, Hellcatpunks, Morrigan, Maxicimam, Algonquins)
Trample Clothing (secondhand)
Usagi Youhinten (secondhand)
XOJapan (Atelier Pierrot, Deorart)

Japanese, non-international shipping:

For these brands, you need to use a shopping service or ask a friend in Japan to order for you. Recommended shopping services includeRinkya and Crescent Shop.

Alice Auaa (gothic)
Algonquins (punk)
And Romeo (gothic, sweet)
Angelic Pretty (sweet) 
arca (classic)
Atelier Angelica (classic, childrenswear)
Atelier Boz (gothic, aristocrat, menswear)
Atelier Pierrot (gothic,classic)
Aya (wa)
Bebe Lota (sweet, casual)
Black Peace Now (gothic, punk, menswear)
Bodyline (sweet, gothic, punk, cheap)
Carroll (classic)
Catherine Cottage (classic, mori, children’s clothes)
Chocochip Cookie (sweet, classic)
Dangerous Nude (ero, sweet, gothic)
Deorart (gothic, punk)
despair (gothic, wa, ero)
Endorphins (gothic) 
Excentrique (classic, corsets)
Flasco (Juliette et Justine, Victorian Maiden, Mary Magdalene, Metamorphose, Excentrique, Innocent World, Atelier Boz, Miho Matsuda, Na+H, etc)
Grimalkin (Algonquins, BPN, Sexpot ReVeNGe, Maxicimam, BPN, yosuke, etc)
Heart E (sweet)
h.Naoto (punk, gothic, menswear)
Jelly Bean (classic)
Katharsis (gothic, classic)
KERA SHOP (… most major brands)
Kikirara Shoten (ero, aristocrat, gothic) 
Kuro Fukuya (gothic, aristocrat)
Maxicimam (sweet, punk)
Melche Shutilforc (classic)
Mezzo Piano (children’s clothes)
Millefleurs/Millenoirs (sweet, gothic, classic) 
Moi-meme-Moitie (egl, ega)
Moon Afternoon/Berry Berry Tea Time (classic, doll’s clothes)
Na+H (gothic, ero)
Pina Sweet Collection (classic) 
Princess Doll (classic)
Putumayo (punk)
Qutie Frash (qi, wa, punk)
RITUALS (punk)
ROCKSHOP S.O.S (Algonquins, Peace Now, Sexpot ReVeNGe, etc)
Rosa Bianca (classic)
Seraphim (gothic, classic)
SEX POT ReVeNGe (punk)
Spica (punk, gothic)
Triple Fortune (classic, gothic, hats)
Victorian Maiden (classic)
YUki (classic, casual)

Auction sites:

As above, you will probably need a shopping service for these sites.

Mbok
Y!Japan

Korean:

Baroque (gothic, classic)
Cloud Chamber (gothic)
Cruel Arcadia (gothic)
Dear Margaret (classic)
Goth Loli Closet (gothic, classic, sweet)
La Vie en Rose (classic)
Maggot (sweet)
Paradise Kiss (sweet)
Rainbow Sherbet (sweet)

Taobao:

Some Taobao stores will accept international orders via email, but most will require a shopping service. Alternatively, several of these brands can be purchased through stores like Qutieland and Clobba Online.

69th Department (gothic, classic)
Akane & Alois (sweet, classic)
AmaStacia (gothic, classic)
Black Tea Lolita (gothic, punk)
Dear Celine (sweet, classic)
Dream of Lolita (sweet, print replicas)
HMHM (sweet, classic)
Ichigo15 (gothic, boystyle)
Infanta (sweet, classic)
Kidsyoyo (classic, sweet)
Kira Kira (classic, gothic)
Krad Lanrete (gothic)
Lace Story (sweet)
Last Country (sweet, gothic)
Lolimaiden (classic)
Lolita Princess (sweet, classic)
Lost Luna (gothic, aristocrat, sweet, boystyle)
MoMo&jia baby (sweet)
Princess Faith (sweet)
Princutess (sweet)
Pyon Pyon (gothic)
R Series (classic, sweet)
Rose Melody (gothic, sweet, classic)
Surface Spell (sweet, gothic)
Westmend (sweet, classic)
White Moon (sweet)
Yolanda (classic, gothic)

Etsy:

Etsy is a site where you can sell handmade and vintage things, it’s great for independent lolita shops.

Bows Before Bros (sweet, plus size)
I Do Declare (classic, gothic)
Icing Sugar (sweet)
Little Macaron (sweet)
Miscy’s Gothic Lolita and Vintage (classic, sweet)
The Snow Field (classic)

Accessories:

These shops sell predominantly jewellery, bags and other accessories that go well with lolita.

6%DOKIDOKI (sweet accessories, jewellery)
Ability Normal (gothic jewellery)
Alice Coorde (classic jewellery)
Angelic Rose (nails)
Annie Antique (sweet, classic jewellery)
Atelier Rose Sound (gothic jewellery)
Aya’s Kawaii Mono Ya San (nails, sweet jewellery)
Baroque Quartz (gothic jewellery)
bitterSWEET (sweets jewellery)
Bitter Sweet (gothic, sweet jewellery)
Bling & Pink (sweets jewellery)
Candygears (minihats)
Celeste Stein (patterned tights)
Chocomint (sweet/deco jewellery, hair accessories, charms…)
Classical Tiara (classic, gothic hair accessories and hats)
Coquettish Tiara (sweet bags)
Curvy’s (sweet, himegyaru, jewellery, hair accessories, goods)
Dark Whisper (gothic, classic accessories)
Green Field (classic jewellery and accessories)
JAJABOON (gothic, punk, jewellery)
Kawaii Goods (hair accessories, jewellery)
Lolitaer (sweet, classic)
Lumiebre (parasols, umbrellas)
Nail Puick (nails)
Paris Kids (jewellery, hair accessories, nails)
Paradise Rose (sweet)
Patisserie Pink (jewellery)
Q-pot. (sweet jewellery)
Rolianne (jewellery, hair accessories)
Secret Shop (socks)
Starchild (jewellery)
Suppurate System (jewellery, mini crowns) 
Swimmer (sweet accessories)
tears heaven (jewellery)
Vivienne Westwood (jewellery, bags, shoes)
Yukiumi (nails, decoden, jewellery, contact lenses)

Shoes:

Every lolita outfit needs appropriate footwear, afterall!

Alice Kingdom (sweet)
an*tai*na (Nana Lolita) (replicas)
an*tai*na (Lolita Cos Punk) (replicas)
an-ten-na (gothic, punk, sweet, rocking horses)
Ling-Lam (Montreal shoes)
Yosuke (punk, gothic)

Wigs:

Some of these places are more cosplay-orientated, however this doesn’t matter so much when you’re looking for a wig. (especially when you want something pastel pink and poofy!)

Alibaba no Tamago
Arda Wigs
Cosplay Wig
Cosplay Wig USA
Cyperous
E-NEW
Elf7
Fantasy Sheep
Gabalnara
KrWig
Laurawu-123
Maple
Prisila
Q More
Silvi
Wigland
Zephyr

Circle Lenses:

Circle lenses are a popular trend in lolita fashion at the moment. Be careful though, with what you’re sticking in your eyes! If in doubt, ask an optician first.

Apple of Your Eye
Circlelens.net
Contactlens Xchange
Eyecandy Lens
I-Beauty Shop
Korea Big Eyes
Pinky Paradise
The Dolly Eye

Momolens

Corsets:

While not an essential part of lolita, a good corset can make your outfit look awesome. Some of these sites contain pictures that aren’t worksafe, so be warned.

Angela Friedman
Angels Carrying Savage Weapons
Axfords
Bibian Blue
Blooddrop
Brute Force Studios
Corset Rouge
Dark Garden
Daze of Laur
Delicious Corsets
Electra Designs
Enchanted Corsets
Exquisite Restraint
Fairy Goth Mother
Gallery Serpentine
Heavenly Corsets
Isabella Corsetry
Jurnecka Creations
Lace Embrace Atelier
Madame le Strange
Maya Hansen
Meschantes
Morgana Femme Couture
Pink Label Corsets
Puimond
Scoundrelle’s Keep
Skeletons in the Closet
Sidney Eileen
Starkers
Sweet Carousel Corsetry
The Twilight Parlour
Timeless Trends
Totally Waisted
Valkyrie Corsets
Vicious Venus
Vollers
Volute Corsets
What Katie Did


Decoden/supplies:

A lot of lolitas are into decoden, that is, the art of covering your electronics with cute designs. The following shops sell premade cases, or supplies to deco your own things.

Decoparts
DecoSweets
Dekoden
Delish Beads
FULLMOON
Mimi Lo Lo
misssapporo
Strapya
Sweet Essence

Fabric/Sewing and Craft Supplies:

If you prefer to sew your own clothes/make your own accessories, there is still something for you~ Here are some shops that sell loliable fabrics, and other supplies.

Beautiful Work
Cotton Chips
Cotton Leaf 
Duckcloth
Emi Craft in Japan
Fabric Tales
From Japan with Love
Funky Fabrix
Girl Charlee Fabrics
Harts Fabric
Japan Lovely Crafts
Karaku
Kimono Flea Market Ichiroya
Kinkado
Matatabi
Okadaya
Pooh-tan
Quilt Gate
Sakura Fabrics
Shabby Fabrics
Spoonflower (custom prints)
Super Buzzy
Yanagiya

Not strictly lolita, but related:

These shops aren’t strictly lolita, so it’s not recommended that you start buying full outfits from them for lolita. However, some of their items can be used with lolita to great effect, or an alternative for when you don’t feel like wearing lolita. Or perhaps you’re interested in other Japanese fashions, from fairy kei, to gyaru, to natural kei, to otome~

Accent (natural kei, second hand)
Amish Farm (natural kei)
Angel Fish (natural kei)
Armoire (natural kei)
Atelier Crochet (natural kei)
Axes Femme (natural kei)
Belindy (natural kei)
Blue Ribbon (natural kei, second hand)
Candy Stripper (punk, sweet)
Cat’s Paw (natural kei)
Chaton (natural kei)
co-cho (antique clothes, lace, fabric)
Cotton Garden (natural kei, second hand)
D’erlanger (natural kei, second hand)
daily style (natural kei select shop)
Dobby (otome)
Emy’s Shop (natural kei, second hand)
Grimoire (dolly kei)
HELLCATPUNKS (punk)
HoneyBlade (natural kei, second hand, some lolita brands as well)
Jane Marple (otome)
Jesus Diamante (himegyaru)
K’s Doll Club (natural kei, second hand)
Listen Flavor (punk)
Little Trunk (natural kei, second hand)
Liz Lisa (casual, himegyaru)
Lois CRAYON (otome)
Lovely Style (natural kei)
maniaQ (fairy kei)
Marchen Melancholic Romance (natural kei)
Milk (otome, casual)
Mina Perhonen (otome)
Pink House (natural kei)
Romantic Standard (natural kei, mori girl)
Shake Shake (gyaru)
SM2 (natural kei)
Spank! (Spank!, fairy kei)
Spank! Shopping (Spank!, fairy kei)
Takuya Angel (wa/cyber)
Wonder Rocket (mori girl, natural kei)

List taken from here