LIST OF EVERY 1998 FURBY!! OH MY!!!
...because I'm unsatisfied with SEO Fandom wikis...

Variations

The original releases of series 1-5 each had 4 variation of eye colors: blue, green, brown, and grey. Series 6-7 had those eye colors plus 3 additional ones: neon blue, neon green, and silver.

International Info

U.S.A: Furby. ~$35.00 USD. UPC: 050626006603 game.com page, furby.com page
Canada: Furby. Box is in English and Canadian French. UPC: 050626006603
Japan: ファービー. Distributed by Tomy. Tomy Official Furby Site (Archived). UPC: 4904810559221
Spanish Speaking Countries: Furby. 1998 Furby Page (Archived)
Germany: Furby. UPC: 5023117481970. 1998 Furby Page (Archived)
Italy: Furby. Distrubuted by GiG. UPC: 050626014622
France: Furby. UPC: 050626014608

Series 1

Series 2

Series 3

Series 4

Coinciding with the release of Furby Babies, series 4 was released in September 1999 for $??.00 USD.

Image Names
Ladybug (Common fan name)
Tentoumushi, Furby Club translates this as "LADYBIRD". (てんとう虫) (Tomy site "common name", Furby Club Official Guidebook Vol. 3)
Dragon (Common fan name)
Dragon (ヂラゴン) (Tomy site "common name", Furby Club Official Guidebook Vol. 3)
Tie Dye (Common fan name)
Garcia* (ガルシア) (Tomy site "common name", Furby Club Official Guidebook Vol. 3)
Coffee (Common fan name)
Coffee (コーヒー) (Tomy site "common name", Furby Club Official Guidebook Vol. 3)
Bumble Bee (Common fan name)
Hachi, Furby Club translates this as "BEE". (ハチ) (Tomy site "common name", Furby Club Official Guidebook Vol. 3)
Cheetah (Common fan name)
Cheetah (チーター) (Tomy site "common name", Furby Club Official Guidebook Vol. 3)

* It is unclear to me why this one is named Garcia in Japan. Japanese Twitter user "Little_iFurby" proposes that it's named after the asteroid Garcia, inturn named after psychedelic band "Grateful Dead" guitarist Jerry Garcia.

Series 5

TBA.

Image Names
Rooster (Common fan name)
Ondori, lit. Rooster (オンドリ) (Tomy site "common name")
Turtle (Common fan name)
Turtle (タートル) (Tomy site "common name")
Kiwi (Common fan name)
Kiwi (キウイ) (Tomy site "common name")
Sherbert (Common fan name)
Sherbert (シャーベット) (Tomy site "common name")
Koala (Common fan name)
Koala (コアラ) (Tomy site "common name")
Lizard (Common fan name)
Lizard (リザード) (Tomy site "common name")

Series 6

TBA.

Image Names
Alligator (Common fan name)
Alligator (アリゲーター) (Tomy site "common name")
Blue Turtle (Common fan name)
Blue Turtle (ブルータートル) (Tomy site "common name")
Color Change (Common fan name)
Color Change (カラーチェンジ) (Tomy site "common name")
Champagne (Common fan name)
Champagne (シャンペン) (Tomy site "common name")
Tart Tangerine (Common fan name)
Tangerine (タンジェリン) (Tomy site "common name")
Husky (Common fan name)
Husky (ハスキー) (Tomy site "common name")

Series 7

TBA.

Image Names
Red Wolf (Common fan name)
Gold Stripes (Common fan name)
Gold Stripe (ゴールドストライプ) (Tomy site "common name")
Banana Skin (Common fan name)
Banana Peel (バナナピール) (Tomy site "common name")
Raccoon (Common fan name)
Raccoon (ラクーン) (Tomy site "common name")
Juicy Grape (Common fan name)
Mink (Common fan name)
Mink (ミンク) (Tomy site "common name")

Series 8

TBA.

Image Names
Puppy Dog (Common fan name)
Rusty Dots (Common fan name)
Green Bean (Common fan name)
Blueberry (Common fan name)
Labrador (Common fan name)
Penguin (Common fan name)

Special Editions

Image Names Model Release Barcode Notes
Your Royal Majesty (Box sticker)
Royal Furby, King Furby (Common fan name)
70-794 TBA
136,000 pieces
U.S.A: 050626020159 N/A
Spring, Easter (Common fan name)
Spring (スプリング) (Tomy site "common name", Furby Club Official Guidebook Vol. 1)
70-880 March 2000 (JP)
? (U.S.A), 250,000 pieces
U.S.A: 050626015803 N/A
Spring Time (Common fan name)
Spring (スプリング) (Furby Club Official Guidebook Vol. 2)
70-884 April 1999, 250,000 pieces (U.S.A) U.S.A: 050626012369 The first limited edition Furby.
Santa (Common fan name)
Christmas (クリスマス) (Tomy site name)
70-885 TBA U.S.A: 050626012451 N/A
Millenium Furby (Sash, tag)
Millenium Furby V1 (Common fan name)
Year 2000 (2000年) (Tomy site name, box title)
70-894 August 20th, 1999, 30-50,000 pieces; Shopko exclusive (U.S.A)
U.S.A: 050626012222
JP: 4904810567400
Each Furby is individually numbered.
While the official Furby website states 30,000 were made, the tag states there are 50,000.
Year 2000 Furby (Sash)
Millenium Furby (Tag)
Millenium Furby V2, Y2K Furby (Common fan name)
70-894 November 1999, 220,000 pieces (U.S.A) U.S.A: 050626012222 N/A

Official Few of a Kinds

Furbys with less than 10 in existance.

Image Names Release
Bejeweled Furby (FAO Schawrz Website)
Jeweled Art Furby (Furby Official Trainer's Guide)
$100,000 USD
FAO Schawrz exclusive
Designed by Sidney Mobell, a portion of the proceeds from this Furby went to Hasbro Children's Hospital. It is unknown how many are in existance, though an unsourced Facebook comment states there are 5. Currently the only confirmed owner is vanna_norwood on Reddit.
Image Names Release
Rainbow Furby (Common fan name) Contest prize

In 2000, Tiger held a "Design-Your-Own-Furby" sweepstakes, where children could create and submit a design, and if chosen, be voted on. The grand prize winner would have their Furby created and given to them while on a tour of the Furby Design Studio in Chicago, Illinois. The winner was "Brittany from Missouri."

Notes

The term for each Furby release seems to vary. I've come across 'waves', 'editions', 'series', 'generations', and 'eras'. I'm using 'series' as that is what was used on the official 1998 site.

Sources

Official Furby Collectibles Guide (Archived)
Furby Official Trainer's Guide by J. Douglas Arnold
Furby Club オフィシャル ガイドブック Vol. 1 (Furby Club Official Guidebook Vol. 1)
Computer Intelligence with Fur | WIRED
FAO Schwarz Bejeweled Furby Listing (Archived)
Bejeweled Furby Facebook comment
Furby Contest Page (Archived)
The Furbish Times/FurbylandNews (Archived)
The Furbish Times/FurbylandNews(Archived, alternate link)
Mystic Fortress - Electronic Furby
vanna_norwood's Bejeweled Furby
Furby Goes International: Japanese Children Captivated By Furby! - June 8, 1999
1999 Google Groups post discussing the release of Furby in Spain
1999 Google Groups post discussing the release of Furby in Germany
German Furby Release Announcement - March 19th, 1999
German Furby General Release and Celebration Announcement
Spring & Graduation JP page.
Spanish-speaking Furby makes Latin America debut
Spring Furby on the official Furby website (Archived)