Although the list below is a constant work in progress, I hope you will find it useful. Let me know if you see punch-card models that are missing.
Also, if you are new to machine knitting on flatbed machines, and you just got a machine, consider the beginner-friendly projects I recommended to all my students and customers.
Unless specified, all machines below accept punchcards with 24-holes (to knit in 24-stitch repeat patterns).
Brother
Bulky:
Brother KH260, 9 mm
Standard:
All standard Brother knitting machines are 4.5 mm-gauge.
Brother KH800, 12-stitch, with a ratchet tool
Brother KH801, 12-stitch, with a ratchet tool
Brother KH811, also pushbutton
Brother KH838
Brother KH868
Brother KH871 with built-in knit leader
Brother KH880
Brother KH881, with built-in knit leader
Brother KH891, with built-in knit leader
Brother KH893, with built-in knit leader
Defendi
Defendi KM2000, standard-gauge, 24-stitch punch card
Elena
(Toyota) Elena 7, standard
(Toyota) Elena Auto 7, standard
Defendi KM3000, with built-in knit leader
Elna
Elna EK2300, bulky, 9 mm, 12-hole punchcards
Empisal
All Empisal knitting machines, to the best of my current knowledge, are under the Empisal Knitmaster brand name.

Empisal Knitmaster 260, standard
Empisal Knitmaster SK-313, standard
Empisal Knitmaster 321, standard
Empisal Knitmaster 323, standard
Empisal Knitmaster 324, standard
Empisal Knitmaster 326, standard, built-in knit leader
Empisal Knitmaster 328, standard
Empisal Knitmaster 329, standard
Empisal Knitmaster 360K, standard, built-in knit-leader
Empisal Knitmaster mod. 600, standard
Empisal Knitmaster 700K, standard, built-in knit leader, built-in intarsia
Empisal Knitmaster mod. 700, standard, built-in knit-leader, built-in intarsia
JUKI
All JUKI standard machines are 4.5 mm gauge.
JUKI KE-1200, Hi-Memory, 12-pushbutton/12-hole punchcard combo
JUKI KE-1500, Hi-Memory, 12-pushbutton/12-hole punchcard combo
Juki KE-2400, 24-hole punchcards, standard
JukI KE-2500, 24-hole punchcards, standard
KnitKing
Standard:
KnitKing KH881, built-in knit leader
KnitKing KH891, built-in knit leader
KnitKing KK91, built-in knit leader
KnitKing KK93, built-in knit leader
BULKY:
KnitMaster
Knitmaster 260, standard
Knitmaster SK313, standard
Knitmaster 321, standard
Knitmaster 323, standard
Knitmaster 324, standard
Knitmaster 326, standard, built-in knit leader
Knitmaster 360K, standard, built-in knit-leader
Knitmaster mod. 600, standard
Knitmaster 700K, standard, built-in knit-leader, built-in intarsia
Knitmaster mod. 700, standard, built-in knit-leader, built-in intarsia
RICCAR
To the best of my knowledge, all RICCAR knitting machines are standard gauge (4.5 mm) and work with 24-stitch repeat patterns/punchcards.
Riccar RK-704K, built-in knit-leader
Riccar RK-705K, built-in knit-leader
Riccar RK-706K, built-in knit-leader
Riccar RK-707
Riccar RK-708, built-in knit leader
Riccar LECLE, foldable
Silver
STANDARD:

All standard-gauge punch-card knitting machines under the Silver brand work with 24-hole punchcards and are of 4.5 mm gauge.
Silver SK250L, lace only
Silver SK322, built-in knit-leader
Silver SK325, built-in knit-leader
Silver SK326, built-in knit-leader
Silver SK327, built-in knit-leader
Silver SK328, built-in knit-leader
Silver SK330, built-in knit-leader
Silver SK360, built-in knit-leader
Silver Reed

Bulky:
All bulky punch-card knitting machines under the Silver Reed brand work with 12-hole punchcards and are of 9 mm gauge.
Silver Reed SK155
Silver Reed SK155P, My Studio
standard:
All standard-gauge punch-card knitting machines under the Silver Reed brands work with 24-hole punchcards and are of 4.5 mm gauge.
Silver Reed 250L
Silver Reed SK360, built-in knit-leader
Silver Reed SK700, built-in knit-leader
Silver Reed SK700N, built-in knit-leader
FINE:
All Silver Reed fine-gauge machines are of 3.6 mm gauge. The punchcard reader accepts cards with up to 30 holes (to knit a 30-stitch repeat pattern).
Silver Reed F270
Silver Reed F370
Silver Reed SK370, built-in knit-leader
Singer
Bulky:
All bulky punch-card knitting machines under the Singer brand work with 12-hole punchcards and are of 9 mm gauge.
Singer mod. 155
Standard:
All standard-gauge punch-card knitting machines under the Singer brand work with 24-hole punchcards and are of 4.5 mm gauge.
Singer MK70, plastic bed, foldable
Singer Cardmatic 313
Singer mod. 313
Singer MemoMatic 322, built-in knit-leader
Singer MemoMatic 328, built-in knit-leader
Singer MemoMatic 360K, built-in knit-leader
Singer MemoMatic 700K, built-in intarsia and knit-leader
Singer mod. 700, built-in intarsia and knit-leader
Singer mod. 740, built-in knit-leader
Studio
Bulky:
All bulky machines under the Studio brand are of 9-mm gauge and work with 14-hole punchcards.
Studio mod. 155
Standard:
All standard-gauge punch-card knitting machines under the Studio brand work with 24-hole punchcards and are of 4.5 mm gauge.
Studio SK312, Cardmatic
Studio mod. 322, built-in knit-leader
Studio mod. 326, built-in knit-leader
Studio mod. 327, built-in knit-leader
Studio mod. 328, built-in knit leader
Studio mod. 360K, built-in knit-leader
Studio mod. 600, built-in intarsia
Studio mod. 700, built-in intarsia, built-in knit-leader
Studio by White SK740, built-in knit-leader
Toyota
All Toyota knitting machines accept 12-stitch punchcards unless specified below.
Toyota Elena 7, standard
Toyota Elena Auto 7, standard
Toyota K600, standard
Toyota 700, standard
Toyota KS727, standard
Toyota KS747, standard
Toyota KS757, standard
Toyota KS777, standard
Toyota KS787, standard
Toyota KS858, standard
Toyota KS895, standard
Toyota KS901, standard
Toyota KS950, standard
Toyota KS650, bulky