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).

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 KH838
Brother KH871 with built-in knit leader
Brother KH881, with built-in knit leader
Brother KH891, with built-in knit leader
Brother KH893, with built-in knit leader
Brother KH811, also pushbutton
Brother KH880
Defendi
Defendi KM2000, standard-gauge, 24-stitch punch card
Defendi KM3000, with built-in knit leader
Elena
(Toyota) Elena 7, standard
(Toyota) Elena Auto 7, standard
Elna
Elna EK2300, bulky, 9 mm, 12-hole punchcards
Empisal
Empisal Knitmaster mod. 155, bulky
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 standard 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
BULKY:

KnitKing KH891, built-in knit leader
KnitKing KK91, built-in knit leader
KnitKing KK93, built-in knit leader
KnitMaster
Knitmaster mod. 155, bulky
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
All RICCAR machines are 4.5 mm gauge 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 RK-708A, built-in knit leader
Riccar 709, 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.
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 Singer bulky punch-card knitting machines 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 Studio punchcard-based bulky machines are of 9-mm gauge and work with 12-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
Some Toyota knitting machines accept 12-stitch punchcards and some 24-stitch.
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