This is a (hopefully) complete list of the light and medium artillery used by or projected for the Wehrmacht, compiled by Antonio Pena with additional info from the other members of the forum.
Guns of 12.8 cm and higher will be classed as heavy artillery. The classification is only mine, the Wehrmacht classified many guns and howitzers of 10.5 cm as heavy (schwere), and had weapons of 15.0 cm at divisional level, so the classification is often imprecise, and other Armies have a different classification.

German Weapons
7.5 cm FK 16 nA (old WW1 guns, 7.7 cm, with new barrels of 7.5 cm)
7.5 cm FK 18 (not standard issue)
7.5 cm FK 38 (ordered by Brazil, but others made for the Wehrmacht)
7.5 cm FK 7M85 (made with barrel of PAK-40 and carriage of the FH-1
7.5 cm FK 7M59 (PAK 40 with increased elevation)
7.5 cm FK WFK L/42 (prototype only)
10.5 cm lFH 16 (old WW 1)
10.5 cm lFH 18 (standard German equipment)
10.5 cm lFH 18 M (FH-18 with muzzle brake and modified recoil system)
10.5 cm lFH 18/39 (ex-dutch guns, barrel replaced with standard FH 18M)
10.5 cm lFH 18/40 (FH-18 M barrel on PAK 40 Carriage)
10.5 cm lFH 18/42 (modified FH-18, proptotype only)
10.5 cm lFH 42 (development of the FH-18, not accepted for service)
10.5 cm lFH 43 Skoda (prototype only)
10.5 cm lFH 43 Krupp (FH 18/42 barrel on PAK 43 carriage, prototype)
10.5 cm K 41 (Prototype only)
10.5 cm sK 18 (standard equipment)
10.5 cm sK 18/40 (10.5 cm K 40 barrel on sK 18 carriage)
10.5 cm sK 42 (new name for the sK 18/40)
12.8 cm K 44 Krupp (in production, but no one reached front line)
12.8 cm K 44 Rheinmetall (not accepted for production)
12.8 cm K 81 (New weapon under development)
12.8 cm K 81/1 (K 81 barrel on carriage of the french 155 GPF-T)
12.8 cm K 81/2 (K 81 barrel on carriage of the russian M-37-15.2 cm)

Captured Weapons
7.5 cm FK 01 (n) (ex-norwegian M-01 Erhardt)
7.5 cm FK 02/26 (p) (ex polish vz 26, old russian M-00, relined)
7.5 cm FK 17 (t) (ex-czech M-28 Skoda)
7.5 cm FK 97 (p) (ex-polish M-97)
7.5 cm FK 231 (f) (ex-french M-97)
7.5 cm FK 232 (f) (ex french M-97, modified with split trail carriage)
7.5 cm FK 234 (b) (ex-belgian FK-16nA relined to 7.5)
7.5 cm FK 235 (b) (ex-belgian M-05 TR, Krupp design of 1905)
7.5 cm FK 236 (b) (ex-belgian FK-16 nA, relined to 7.5)
7.5 cm FK 237 (i) (ex-italian licence built Krupp M-06)
7.5 cm FK 243 (h) (ex-dutch M-02/04, licence built Krupp M-03)
7.5 cm FK 244 (i) (ex-italian M-11 Deport)
7.5 cm FK 245 (i) (ex-italian M-12, modified M-06)
7.5 cm FK 246 (n) (ex-norwegian M-01 Erhardt)
7.5 cm FK 247 (n) (ex-norwegian M-01)
7.5 cm FK 248 (i) (ex-italian M-37 Ansaldo)
7.5 cm FK 249 (j) (ex-Yugoslav Schneider Mle 12 gun)
7.5 cm lFH 255 (i) (ex-italian M-35)
7.62 cm FK 288 (r) (ex–russian M-42/ZIS-3)
7.62 cm FK 288/1 (r) (ex-russian M-41)
7.62 cm FK 290/1 (r) (ex russian M-02/06)
7.62 cm FK 295/1 (r) (ex-russian M-02/30, L/30)
7.62 cm FK 295/2 (r) (ex-russian M-02/30, L/40)
7.62 cm FK 296 (r) (ex-russian M-36, used also as PAK-36 and FK-36)
7.62 cm FK 297 (r) (ex-russian M-39, used also as PAK-39 and FK-39)
7.62 cm FK 305 (r) (ex-russian M-43)
7.62 cm FK 310 (r) (ex-russian M-02/30)
7.65 cm FK 05/08 (ö) (ex-austrian M-05/08 Skoda)
7.65 cm FK 17 (ö) and (t) (ex-austrian and ex-czech M-17 Skoda)
7.65 cm FK 18 (ö) (ex-austrian M-18 Skoda)
7.65 cm FK 300 (j) (ex-jugoslavian M-05/08 Skoda)
7.65 cm FK 303 (j) (ex-jugoslavian M-17 Skoda)
7.65 cm FK 304 (j) (ex-jugoslavian M-28 Skoda)
8.0 cm FK 18/17 (t) (ex-czech M-?)
8.0 cm FK 30 (t) (ex-czech M-30)
8.38 cm FK 271 (e) (ex-british QF 18 pr Mk I-II on carriageMk II PA)
8.38 cm FK 272 (e) (ex-british QF 18 pr Mk I-II on carriage ?)
8.38 cm FK 273 (e) (ex-british QF 18 pr Mk I-II on carriage ?)
8.38 cm FK 274 (e) (ex-british QF 18 pr Mk I-II on carriage ?)
8.38 cm FK 305 (r) (ex-russian 8.5 cm M-43g)
8.76 cm FK 280 (e) (ex-british QF 25 pr Mk II-III)
8.76 cm FK 281 (e) (ex-british QF 25 pr Mk I on carriage Mk IVp )
8.76 cm FK 282 (e) (ex-british QF 25 pr Mk I on carriage Mk Vp)
10.0 cm lFH 14 (ö) (ex-austrian M-14 Skoda)
10.0 cm lFH 14/19 (p) and (t) (ex polish and ex-czech M-14/19 Skoda)
10.0 cm lFH 30 (t) (ex-czech M-30 Skoda)
10.0 cm lFH 315 (j) (ex-jugoslavian M-14 Skoda)
10.0 cm lFH-316 (j) (ex-jugoslavian M-14/19 Skoda)
10.0 cm lFH-317 (j) (ex-jugoslavian M-28 FE)
10.0 cm lFH 318 (g) (ex-greek M-14/19 Skoda)
10.5 cm FK 17 and 17/04 (ö) (ex-austrian M-04/17 or K-17)
10.5 cm FK 29 (p) (ex polish M-29, modified french M-13 Schneider)
10.5 cm K 35 (t) (ex-czech M-35)
10.5 cm FK 320 (i) (ex-italian M-15 Skoda)
10.5 cm lFH 322 (f) (ex-french M-?)
10.5 cm lFH 323 (f) (ex-french M-?)
10.5 cm lFH 324 (f) (ex-french M-34 Schneider)
10.5 cm lFH 325 (f) (ex-french M-35B)
10.5 cm lFH 326 (i) (ex-italian Obice 105/14 Ansaldo)
10.5 cm lFH 327 (b) (ex-belgian Obusier de 105 GP, ex-German lFH16)
10.5 cm FK-331 (f) (ex-french M-13 Schneider)
10.5 cm FK-332 (f) (ex-french M-36 Schneider)
10.5 cm FK 333 (b) (ex-belgian M-13, french M-13 Schneider)
10.5 cm FK 334(h) (ex-dutch 10.5 cm M-?)
10.5 cm FK 335 (h) (ex-dutch M-27 Bofors)
10.5 cm FK 336 (i) (ex-Italian Cannone da 105/40 Mod. 42)
10.5 cm FK 338 (i) (ex-italian M-13, french M-13)
10.5 cm K 339 (j) (ex-jugoslavian M-36)
10.5 cm K 348 (r) (ex-russian M-?)
10.5 cm K 349 (r) (ex-russian M-?)
10.5 cm K 350 (r) (ex-russian M-?)
10.7 cm K 352 (r) (ex-russian M-10/30)
10.7 cm K 353 (r) (ex-russian M-40)
11.4 cm lFH 361 (e) (ex-british QF 4.5 inch, MkII)
11.4 cm K 365 (e) (ex-british BL 4.5 inch gun Mk II
11.5 cm lFH 362 (r) (ex-russian M-?, british QF 4.5 inch, MkII)
12.0 cm K 370 (b) (ex-belgian canon de 120 L m-31)
12.0 cm lFH 373 (h) (ex-dutch 12 cm L14 Bofors)
12.0 cm lFH 375 (n) (ex-norwegian 12 cm M 09 Rheinmetall)
12.0 cm lFH 376 (n) (ex-norwegian 12 cm M 13 Kongsberg)
12.2 cm sFH 385 (r) (ex-russian M-09/30)
12.2 cm sFH 386 (r) (ex-russian M-09/30g)
12.2 cm sFH 387 (r) (ex-russian M-09/30g)
12.2 cm sFH 388 (r) (ex-russian M-10/30)
12.2 cm K 390/1 (r) (ex-russian M-31)
12.2 cm K 390/2 (r) (ex-russian M-31/37)
12.2 cm sFH 396 (r) (ex-russian M-3
12.7 cm K 382 (e) (ex-british BL 60 pr Mk II)
FK: Feldkanone (field gun)
lFH: leichter Feldhaubitze (light field howitzer)
sK: Schwere Kanone (heavy gun)
K: Kanone (Gun)

The Weapons made in Czechoslovakia after the German take over are classified as German.

NOTE: The following guns are not correctly identified, please help to identify:
8.0 cm FK 18/17 (t) (ex-czech M-?)
8.38 cm FK 272 (e) (ex-british QF 18 pr Mk ? on carriage ?)
8.38 cm FK 273 (e) (ex-british QF 18 pr Mk ? on carriage ?)
8.38 cm FK 274 (e) (ex-british QF 18 pr Mk ? on carriage ?)
8.38 cm FK 305 (r) (ex-russian 8.5 cm M-43g)
10.5 cm lFH 322 (f) (ex-french M-?)
10.5 cm lFH 323 (f) (ex-french M-?)
10.5 cm FK 334(h) (ex dutch M-?, maybe the FH-18 selled by Germany)
10.5 cm K 348 (r) (ex-russian M-?)
10.5 cm K 349 (r) (ex-russian M-?)
10.5 cm K 350 (r) (ex-russian M-?)
11.5 cm lFH 362 (r) (ex-russian M-?, british QF 4.5 inch, MkII)

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