This is a (hopefully) complete list of the SMGs used by the Wehrmacht, compiled by Logan Hartke (using "Guns of the Reich: Firearms of the German Forces, 1939-1945" by George Markham) with additional info from the other members of the forum.

MP.18,I (WWI Bergmann)
MP.28 (improved MP.18,I)
MP.30 (ö) (ex-Austrian S1-100 variant)
MP.34 (ö) (ex-Austrian Steyr Solothurn)
MP.34 Bgm. (Bergmann)
MP.35 (Bergmann version of the MP.34 Bgm.)
MP.38 (Predecessor to the MP40)
MP.38/40 (produced as production of the MP.40 was starting, this model had elements of both designs)
MP.40 (the standard SMG)
MP.40/II (MP40 w/ dual magazine)
MP.41 (MP.40 w/ MP.28-like stock)
MP.44 / MP.43 (StG. 44) (classified as a submachine gun at the time but is more accurately an assault rifle)
EMP44 (cheapy weapon made by Erma at the end of the war; it wasn't any good)
MP.704(f) (ex-Frence PM Vollmar Erma)
MP.715(r) (PPD 34/38)
MP.716(r) (PPD 40)
MP.717(r) (PPSh 41)
MP.719 (r) Captured Russian PPs-43
MP.722 (f) Captured French Mas-38
MP.738 (i) Beretta model 38/42
MP.739(i) (Beretta Mo.938)
MP.740(b) (ex-Belgian Mi.Schmeisser-Bayard Mle.34)
MP.741 (d) (The license built Bergman made in Denmark)
MP.746 (d) (Madsen M-42)
MP.749 (e) Captured British Sten Mk II
MP.751 (e) Captured British Sten Mk II with silencer
MP.760 (e)/(j)/(a)/(r) Captured Thompson M-28 from British, US, Yugoslavian or Soviet)
MP.761 (f) Captured Thompson M-1921 purchased by France in 1939
MP.3008 (German near-copy of the Sten Mk.II made at the end of the war)
MP.E (Erma)

Also used:
Czech ZK 383
Captured LL - Model 50 and Model 55 Reisings
Captured LL and OSS - UD M42
Captured US - M3/M3A1 "Grease Guns"
Finnish Suomi m/31
Hungarian 39.M and 43.M
Romanian M1940 and M1941 Orita
Captured GB - Lanchester
Danish Madsen M/41 (a licence manufactured variant of Suomi KP/-31)