This is a (hopefully) complete list of the mortars used by the Wehrmacht, compiled by Antonio Pena with additional info from the other members of the forum.

le GrW leichte Granatwerfer (light mortar)
GrW Granatwerfer (Mortar)
NbW Nebelwerfer (Smoke Launcher)
MW Minenwerfer (Mortar)
lLdW leichte Ladungswerfer (light demolition charge launcher)
sLdW schwere Ladungswerfer (heavy demolition charge launcher)

German Weapons
5.0 cm le GrW 36 Standard light mortar at the start of war, after 1942 used only by second line and training units
5.0 cm le Gr W 40 S Projected in 1943, after the battle of Stalingrad for use in street fight very few built
8.14 cm GrW 34 Standard medium mortar, in use from 1934 until end of the war
8.14 cm GrW 42 Shorter version of the GrW 34, intended originally for airborne troops use, but gradually replaced the lGrW 36 as light mortar
10.0 cm Gr W/Druckluftwerfer Compressed airoperated mortar. Only two prototypes completed. Also called Gerät 170
10.5 cm NbW 35 Standard smoke and chemical mortar used by the Nebetruppen, after 1941 replaced by the Nebelwerfer but continues in use as conventional mortar
10.5 cm Nbw 51and 52 Only three examples of each model issued for troop trials. Not adopted for service
10.5 cm Nbw 40 Designed as replacement of the NbW 35, entered service in 1940 but very few made. Very heavy and unusual due to his breech loading mechanism
12.0 cm GrW 42 A copy of the 12.0 cm russian mortar M 38, altered only to suit the German production methods. Very popular between front line troops and one of the most effctive weapons in the hands of the infantry
15.0 cm GrW 43 Recoilles mortar developed by Skoda, tested but not adopted for service. Also called 15.o cm Minenwerfer 30/600
20.0 cm l LdgW An specialized spigot mortar (diameter of the spigot 9.0 cm) used by the engineer troops
21.0 cm GrW 69 Designed by Skoda in 22.0 cm, as 22 cm schere Granatwerfer B14, later changed to 21.0 cm, some 200 build after 1944
30.5 cm s Gr W Designed in early 1945 and prototype ready in April, not used in combat
38.0 cm s LdgW Designed also for assault engineers but very few build, due to weight and the need of a carefful emplacement
42.0 cm s Gr W Design started in 1945, after the WW 2 used by the czechs for trials in 1946

Captured Weapons
3.7 cm Spatengranatwerfer (r) (ex-russian weapon that when not in use resembled a conventional spade)
4.5 cm GrW 176 (i) (ex-italian morter de 45/5 M 35 “Brixia”)
4.6 cm GrW (p) (ex-polish M 36, limited use by German troops)
5.0 cm GrW 201 (b) (ex-belgian lance grenades de 50 mm DBT, very few in use and only in second line and training units)
5.0 cm GrW 203 (f) (ex-french lance grenades de 50 M 37, very small and with too short range)
5.0 cm GrW 205/1 (r) (ex-russian 50 mm PM 3)
5.0 cm GrW 205/2 (r) (ex-russian 50 mm PM 39)
5.0 cm GrW 205/3 (r) (ex-russian 50 mm PM 40)
5.0 cm GrW 200 (r) (ex-russian 50 mm PM 41)
6.0 cm GrW 225 (f) (ex-french lance grenades de 60 M 35, used only by second line and training units in France)
8.13 cm GrW 36 (t) (ex-czech minomet M 36, this weapon have a rare automatic loading drum with 6 bombs fixed to the muzzle, but not many in use)
8.14 cm GrW (n) (ex norwegen 81 mm M35 Bombekaster)
8.14 cm GrW 31 (p) (ex-polish M 31, licence built french mortar M 27/31 Brandt)
8.14 cm GrW 33 (ö) (ex-austrian M 33, licence built french mortar M 27/31 Brandt)
8.14 cm GrW 270 (j) (ex-jugoslavian M 31/38 licence built french mortar M 27/31 Brandt)
8.14 cm GrW 270/1 (f) (ex-french mortier de 81 M 27/31 Brandt)
8.14 cm GrW 275 (d) (ex-danish M L/12 licence built french mortar M 27/31 Brandt)
8.14 cm GrW 276 (i) (ex-italian mortero da 81/14 M 35, licence built french mortar M 27/31 Brandt)
8.14 cm GrW 278 (t) (ex-czech minomet M 33, licence built french mortar M 27/31 Brandt)
8.14 cm GrW 278/1 (f) (another designation for the ex-french mortier de 81 M 27/31 Brandt)
8.14 cm GrW 286 (h) (ex-dutch mortier van 8, licence built french mortar M 27/31 Brandt)
8.2 cm GrW 274/1 (r) (ex-russian 82 mm PM 36, russian copy of the french M 27/31 Brandt)
8.2 cm GrW 274/2 (r) (ex-russian 82 mm PM 37, revision of the basic design of the previous mortar with recoil spring between tube and bipod)
8.2 cm GrW 274/3 (r) (ex-russian 82 mm PM 41, new revision of the designable to take 2 small wheels in the bipod, a next step with the wheels fixed to the bipod was called 82 mm PM 43, german designation unknown)
9.0 cm GrW (t) (ex-czech lehky minomet M-17, old weapon used mainly as static weapon)
10.7 cm Geb GrW 328 (r) (ex-russian mountain mortar PBHM 38, produced specifically for mountain troops)
12.0 cm GrW 378 (r) (ex-russian HM 38, one of the best mortar designs of the war, widely used by the germans)
12.0 cm GrW 379 (r) (ex-russian HM 40, a development of the HM 3)
14.0 cm MW 18 (t) (ex-czech hruby minomet M-18, used mainly as static weapon)