I've tried to only include composers whose music has personal significance to me, so you can see where my biases lie. Could potentially cut this list down a bit.
Medieval/Renaissance - I'm never sure who the well known composers here are, but will assume most people will have heard of Hildegard, Machaut, Dufay, Josquin, Palestrina, Tallis etc
John Dunstaple
Philippe de Vitry
Matteo da Perugia
Alexander Agricola
Nicolas Gombert
John Browne
Robert Fayrfax
Luca Marenzio
Cristóbal de Morales
Francisco Guerrero
Jan Pieterszoon Sweelinck
Thomas Tomkins
Baroque - i.e. Bach, Handel, Telemann, Vivaldi, Rameau, etc
Louis Couperin
Girolamo Frescobaldi
Johann Jakob Froberger
Élisabeth Jacquet de la Guerre
Heinrich Ignaz Franz Biber (possibly not that obscure anymore)
Biagio Marini
Marin Marais (also possibly not that obscure, if only due to the movie)
Jean de Sainte-Colombe (Sr.)
Robert de Visée
Marc-Antoine Charpentier
Barbara Strozzi
Jan Dismas Zelenka
Jean-Marie Leclair
Classical - i.e. Beethoven, Haydn, Mozart, Boccherini, Gluck
Antonio Soler
Leopold Koželuh [Kozeluch]
Johann Nepomuk Hummel (slightly too well-known to qualify)
Jan Ladislav Dussek
Maria Szymanowska
Ferdinand Ries
Antonín [Anton, Antoine] Rejcha [Reicha] (not obscure if you're a woodwind player)
Ignaz Pleyel
Václav Jan Tomašek
Jan Václav Hugo Voříšek (borderline Romantic)
Early Romantic - i.e. Chopin, Schubert, Schumann, Mendelssohn, Berlioz, Rossini, etc
Theodor Kirchner
Clara Schumann (increasingly less obscure)
Stephen Heller
Louis [Ludwig] Spohr (in moderation)
Fanny Hensel
Jan Křtitel Václav Kalivoda [Kalliwoda]
George Onslow
Franz Berwald
Louise Farrenc
Niels Wilhelm Gade
Mid & Late Romantic - i.e. Brahms, Wagner, Tchaikovsky, Rachmaninov, Dvořák, Sibelius, etc.
Vitězslav Novák
Ernő [Ernst] Dohnányi
Josef Suk
Cécile Chaminade
Mel Bonis
Emmanuel Chabrier (not obscure to opera fans)
(also, the non-operatic music of Charles Gounod and Georges Bizet, who are otherwise too well-known to qualify)
Friedrich Gernsheim
Robert Fuchs
Max Reger (not obscure in Germany)
Karl Goldmark
Eduard Franck
Paul Juon
Alexander von Zemlinsky
Emilie Mayer
Wilhelm Berger
Ferruccio Busoni (not obscure to pianists)
Ethel Smyth
Julius Röntgen
Agathe Backer-Grøndahl
Wilhelm Stenhammar
Anton Arensky
Nikolay Medtner (increasingly less obscure)
Sergei Taneyev
Vasily Kalinnikov
Anatoly Lyadov
Modern - i.e. Stravinsky, Bartók, Schoenberg, Berg, Webern, etc.
Ruth Crawford Seeger
Leo Ornstein
Alberto Ginastera
Edgard Varèse (not that obscure, I guess)
Ernst Krenek
Bohuslav Martinů
Vítězslava Kápralová
Erwin Schulhoff (increasingly less obscure)
Karol Szymanowski (increasingly less obscure)
Sándor Veress
Florent Schmitt
Frank Martin
Jacques Ibert
Egon Wellesz
Artur Schnabel (yes, he also composed)
Boris Blacher
Karl Amadeus Hartmann
Franz Schreker
Federico Mompou
Kaikhosru Shapurji Sorabji
Roberto Gerhard
Nikos Skalkottas
Erik Chisholm
George Enescu (yes, he too also composed)
Rebecca Clarke
Ahmed Adnan Saygun
Goffredo Petrassi
Matthijs Vermeulen
Nikolay Roslavets
Nikolay Myaskovsky
Grażyna Bacewicz
Vytautas Bacevičius
Ivan Vyshnegradsky [Wyschnegradsky]
Nikolay Obukhov [Obouhow]
Vagn Holmboe (not obscure in Denmark)
Rued Langgaard (increasingly less obscure)
Fartein Valen
Hilding Rosenberg
Post-1945 avantgarde - i.e. Cage, Feldman, Xenakis, Ligeti, Stockhausen, Boulez, Nono etc
Earle Brown
Christian Wolff
James Tenney
George Perle
Pauline Oliveros
Robert Ashley
Cornelius Cardew
Elisabeth Lutyens
Harrison Birtwistle
Michael Finnissy
György Kurtág
Emmanuel Nunes
Bernd Alois Zimmermann
Vinko Globokar
Hans Werner Henze
Mauricio Kagel
Henri Pousseur
Heinz Holliger
Jean Barraqué
Franco Donatoni
Maurice Ohana
Hugues Dufourt
Tristan Murail
Gérard Grisey
Aldo Clementi
Salvatore Sciarrino
Cristóbal Halffter
Isang Yun
Hermann Meier
Galina Ustvolskaya
Arne Nordheim
James Dillon
Bryn Harrison
Franck Bedrossian
Iancu Dumitrescu
Ana-Maria Avram
Malin Bång
Ole-Henrik Moe
Milica Djordjević
Adriana Hölszky
Enno Poppe
Chaya Czernowin
Brian Ferneyhough
Liza Lim
Chris Dench
Brice Pauset
Michaël Lévinas
Junghae Lee
Mathias Spahlinger
Dmitri Kourliandski
Clara Iannotta
Johannes Schöllhorn
Rebecca Saunders
Richard Barrett
Alwynne Pritchard
Luca Francesconi
François-Bernard Mâche
Rolf Riehm
Åke Parmerud
Maja S. K. Ratkje
Simon Steen-Andersen
Natasha Barrett
Roland Kayn
Post-1945 traditionalist - i.e. Britten, Copland, Shostakovich, Messiaen, Górecki, Pärt, Adams, Glass, etc
George Rochberg
William Bolcom
Minna Keal
Kenneth Leighton
Edmund Rubbra
Robert Simpson
Witold Lutosławski
Krzysztof Penderecki (maybe not that obscure)
Miloslav Kabeláč
Xavier Montsalvatge
Mieczysław [Moishe, Moses] Weinberg [Vainberg, Vaynberg, Vajnberg] (increasingly less obscure in spite of the ten or twelve different potential name transliterations)
Per Nørgård
Allan Pettersson
Linda Buckley
Bent Sørensen
Poul Ruders
Aaron Kernis
Valentin Silvestrov
Hans Abrahamsen
Lowell Liebermann
Robin Holloway
Gerald Barry
Anders Eliasson
Post-1945 other - i.e. electronic music, polystylists, experimentalists, sound artists & "miscellaneous"
Lou Harrison
Frederic Rzewski
Henry Brant
Terry Riley
Laurence Crane
Howard Skempton
Zygmunt Krauze
Włodzimierz Kotoński
Jo Kondo
Horațiu Rădulescu
Alfred Schnittke
Claude Vivier
Fausto Romitelli
Frank Denyer
Stuart Saunders Smith
Catherine Lamb
Chiyoko Szlavnics
Klaus Lang
Gérard Pesson
Jennifer Walshe
Yannis Kyriakides
Calliope Tsoupaki
James Weeks
Walter Zimmermann
Christopher Fox
José Maceda
Kate Soper
Olivia Block
Éliane Radigue
Evan Johnson
Annea Lockwood
Francisco López
Ikue Mori
Luc Ferrari
Vanessa Rossetto
Mirjam Tally
Julius Eastman
Linda Catlin Smith
John Luther Adams (increasingly less obscure)
