Please note that this is a company listing not a brand listing, for the latter see: Brands & trademarks

Bassoons (Fagotts)
Algam (H/B) — Amati (H) — Beijing Eternal (H) — Beijing Xinghai Piano Group Limited (H) — Bernd Moosmann (H) — Buffet Crampon (B) — Conn-Selmer (H) — GTRC Services (H) — Guntram Wolf (H) — Jiangyin Jiyang Musical Instrument Co. (H) — Mac Corporation (H) — New Star Musical Instrument Co. (H) — Reliance International Corp. (H) — Tianjin Jinbao (H) — Wilhelm Heckel (H).
(H) = Heckel system aka German system - (B) = Buffet system aka French system. Heckel is standard in all countries except France.

Companies that have made bassoons in the past
Henri Selmer Paris.

Fagottinos (Childrens bassoons)
Guntram Wolf — Magilanck
Small bassoons, used as childrens instruments or as alto/tenor instuments in Bassoon ensembles.

Contrabassoons/double bassoons
Amati — Bernd Moosmann.

Contraforte (improved contrabassoon)
Benedikt Eppelsheim — Guntram Wolf.

Dulcians (Reanissance dulcians)
Guntram Wolf
Predecessor to the baroque bassoons and contrabassoons.

Baroque bassoons
Guntram Wolf
The earlest known bassoons and predecessors to the Classic/Early romantic bassoon.

Baroque contrabassoons
Guntram Wolf.

Classic/early romantic bassoons
Guntram Wolf.

Late romantic bassoon
Guntram Wolf.

Romantic/Wiener contrabassoons
Guntram Wolf.

Conservatoire oboes
Beijing Eternal — Beijing Xinghai Piano Group Limited — Buffet Crampon — Conn-Selmer — F. Lorée — GTRC Services — Guntram Wolf — Jiangyin Jiyang Musical Instrument Co. — Mac Corporation — Marigaux — New Star Musical Instrument Co. — Reliance International Corp. — Romeo Orsi
A Conservatoire obeo is what is considered the standard oboe these days and is also known as a modern oboe, French bore, Böhm oboe or Triebert oboe.

Wiener oboes (Viennese oboes)
Guntram Wolf
Note that a Wiener oboe is both a bore and a keying system, most makers of these instruments will make instruemnts that have Wiener bore and key system but also make instruments that have a Wiener bore but feature a Conservatoire keying.

Childrens oboes (small and/or simplified)
Guntram Wolf.

Heckelphon (Baritone oboe)
Wilhelm Heckel.

Lupophone (Bass oboe)
Guntram Wolf.

Bass oboe
F. Lorée — Marigaux.

Oboe d'amore
F. Lorée — Marigaux.

Baroque obo d'amore
Guntram Wolf.

Musette oboe (piccolo oboe)
F. Lorée — Marigaux.

Cor anglais
Buffet Crampon — F. Lorée — Marigaux
Known in the USA as "English horn" but use of this name is discouraged since it is neither English nor a horn.

Renaissance shawms
Charles Collier — Guntram Wolf
A development of the mediaeval shawm and the predecessor to both German shawms and early (baroque) oboes.

German shawn
Guntram Wolf
Developed at the same time as the baroque oboe but is intended for outdoor playing and is thus much louder if less refined.

Baroque oboes
Guntram Wolf.

Classic/early romantic oboes
Guntram Wolf.

Late romantic oboes
Guntram Wolf.

Crumhorns
Kelhorn Corp..

Cornemuses
Paul Beekhuizen
Basically a straight Crumhorn, not to be confused with a Petite Cornamuse or Cornamuse du Centre which are bagpipes.

Kelhorn
Kelhorn Corp.
An instrument meant to sound like a Crumhorn but play like a modern isntrument.

Rackets
Paul Beekhuizen.

Double reeds and cane
Charles Double Reed — Chartier LLC (Oboe only) — Colorado Reed Company — Conn-Selmer — Diamond Musical Products — ETS Rigotti — F. Lorée — Gonzalez Reeds — Kreedo — Lisa's Oboe Reedery — Marzluf Reeds — North Texas Oboe Reed and Cane — Prestini — Razzco (Bassoon only) — Richard Rath — RIMPL — Tianjin Jinbao.

Companies that have made double reeds and cane in the past
Angela Wells — KHS Group — Ricardo Döringer.

Capped double reeds (Crumhorns, Cornamuses etc.)
Kelhorn Corp..

Crooks/bocals for bassoons and bass clarinets
Amati — Bernd Moosmann — F. Lorée — Gloger-Handkraft.