This is the full list of vendor- and product IDs from the gamecontrollerdb.txt file in the TheC64 firmware version 1.3.2. It is unclear whether this is used for both (Mini and Maxi) variants of the emulator by Retro Games Ltd.

The list is sorted on the vendor ID and product ID.

0001:0001  Nintendo Wiimote
0010:0082  Akishop Customs PS360+ v1.66
0078:0006  Microntek USB Joystick
0079:0006  DragonRise Inc. Generic USB Joystick
0079:0006  USB gamepad
0079:0011  Retrolink SNES Controller
0079:0011  USB Gamepad1
0079:181c  SPEEDLINK COMPETITION PRO Game Controller for Android
0079:1843  Mayflash GameCube Controller Adapter
0079:1844  Mayflash GameCube Controller
0079:18d2  MAGIC-NS
0079:18d4  GPD Win 2 Controller
040b:6533  Speed-Link Competition Pro
0428:4001  Gravis GamePad Pro USB 
044f:b300  Thrustmaster Firestorm Dual Power
044f:b312  Thrustmaster vibrating gamepad
044f:b315  Thrustmaster Dual Analog 4
044f:b320  Thrustmaster 2 in 1 DT
044f:b323  Thrustmaster Dual Trigger 3-in-1
044f:b326  Thrustmaster Gamepad GP XID
044f:d008  Thrustmaster Run N Drive Wireless
044f:d009  Thrustmaster Run N Drive Wireless PS3
045e:000e  Microsoft SideWinder
045e:0202  Old Xbox pad
045e:0285  Microsoft X-Box pad (Japan)
045e:0289  Microsoft X-Box pad v2 (US)
045e:028e  Microsoft X-Box 360 pad
045e:028e  Speedlink TORID Wireless Gamepad
045e:028e  SpeedLink XEOX Pro Analog Gamepad pad
045e:028e  X360 Controller
045e:0291  X360 Wireless Controller
045e:02a1  X360 Wireless Controller
045e:02a1  Xbox 360 Wireless Receiver (XBOX)
045e:02d1  Microsoft X-Box One pad
045e:02d1  Microsoft X-Box One pad v2
045e:02dd  Microsoft X-Box One pad (Firmware 2015)
045e:02e0  Xbox One Wireless Controller
045e:02e3  Microsoft X-Box One Elite pad
045e:02ea  Xbox One Wireless Controller
045e:02fd  Xbox One Wireless Controller
045e:0719  X360 Wireless Controller
046d:c20a  Logitech Inc. WingMan RumblePad
046d:c211  Logitech WingMan Cordless RumblePad
046d:c215  Logitech Logitech Extreme 3D
046d:c216  Logitech Dual Action
046d:c218  Logitech RumblePad 2
046d:c219  Logitech Cordless RumblePad 2
046d:c219  Logitech F710 Gamepad (DInput)
046d:c21d  Logitech F310 Gamepad (XInput)
046d:c21e  Logitech F510 Gamepad (XInput)
046d:c21f  Logitech F710 Gamepad (XInput)
047d:4005  Gravis Eliminator GamePad Pro
04b4:010a  CYPRESS USB Gamepad
050d:0803  Nostromo n45 Dual Analog Gamepad
054c:0268  PS3 Controller
054c:05c4  PS4 Controller
054c:09cc  PS4 Controller
054c:0ba0  PS4 Controller
056e:2003  JC-U3613M - DirectInput Mode
057e:0330  Nintendo Wii Remote Pro Controller
057e:2006  Joy-Con (L)
057e:2007  Joy-Con (R)
057e:2009  Nintendo Switch Pro Controller
0583:2060  iBuffalo SNES Controller
05a0:3232  8Bitdo Zero GamePad
05ac:3232  VR-BOX
05fd:3000  InterAct GoPad I-73000 (Fighting Game Layout)
06a3:0109  Saitek P880
06a3:040b  Saitek P990 Dual Analog Pad
06a3:040c  Saitek P2900 Wireless Pad
06a3:f518  Saitek PLC Saitek P3200 Rumble Pad
06a3:f622  Cyborg V.3 Rumble Pad
06a3:f623  Saitek Cyborg V.1 Game Pad
06a3:ff0c  Saitek P2500 Force Rumble Pad
0738:3250  Mad Catz FightPad PRO (PS3)
0738:3384  Mad Catz FightStick TE S+ (PS3)
0738:3480  Mad Catz fightstick (PS3)
0738:4716  Mad Catz Wired Xbox 360 Controller
0738:4738  Mad Catz Wired Xbox 360 Controller (SFIV)
0738:5266  Mad Catz C.T.R.L.R 
0738:8250  Mad Catz FightPad PRO (PS4)
0738:8384  Mad Catz FightStick TE S+ (PS4)
0738:8480  Mad Catz fightstick (PS4)
0738:8818  MadCatz PC USB Wired Stick 8818
0738:8838  MadCatz PC USB Wired Stick 8838
07b5:0315  impact
0810:0001  Twin USB PS2 Adapter
0810:0003  USB Gamepad
0810:e501  NEXT SNES Controller
0925:0005  Sony PS2 pad with SmartJoy adapter
0925:03e8  Mayflash Wii Classic Controller
0925:8866  MP-8866 Super Dual Box
0926:8888  Cyber Gadget GameCube Controller
0955:7210  NVIDIA Controller
0955:7214  NVIDIA Controller v01.04
0b05:4500  ASUS Gamepad
0c12:0005  AxisPad
0c12:0005  Manta Dualshock 2
0c12:0e10  ZEROPLUS P4 Gamepad
0c45:4320  XEOX Gamepad SL-6556-BK
0e6f:011e  Rock Candy PS3 Controller
0e6f:011f  Rock Candy
0e6f:0130  EA Sports PS3 Controller
0e6f:0139  Afterglow Controller for Xbox One
0e6f:0139  Afterglow Prismatic Controller
0e6f:0139  Afterglow Prismatic Wired Controller 048-007-NA
0e6f:0146  Rock Candy Xbox One Controller
0e6f:0164  PDP Battlefield One
0e6f:0213  Afterglow
0e6f:0214  PS3 Controller
0e6f:02a8  PDP Wired Controller for Xbox One
0e6f:0301  Logic3 Controller
0e6f:0401  Gamestop Logic3 Controller
0e6f:0413  Generic X-Box pad
0e8f:0003  PS3 Controller
0e8f:0008  Gasia Co. Ltd PS(R) Gamepad
0e8f:0012  GreenAsia Inc. USB Joystick
0e8f:1006  GreenAsia Electronics 4Axes 12Keys GamePad 
0e8f:3013  HuiJia SNES Controller
0f0d:0009  Natec Genesis P44
0f0d:000d  hori
0f0d:0010  HORI CO. LTD. FIGHTING STICK 3
0f0d:0022  HORI CO. LTD. REAL ARCADE Pro.V3
0f0d:005e  Hori Fighting Commander 4 (PS4)
0f0d:005f  Hori Fighting Commander 4 (PS3)
0f0d:0066  HORIPAD 4 (PS4)
0f0d:0067  HORIPAD ONE
0f0d:006a  HORI CO. LTD. Real Arcade Pro.4
0f0d:006b  HORI CO. LTD. Real Arcade Pro.4
0f0d:006e  HORIPAD 4 (PS3)
0f0d:0092  Hori Pokken Tournament DX Pro Pad
0f0d:00ee  HORIPAD mini4
0f30:010b  Jess Tech GGE909 PC Recoil Pad
0f30:0110  Jess Tech Dual Analog Rumble Pad
0f30:1112  QanBa Arcade JoyStick
11c9:55f0  HJC Game GAMEPAD
11ff:3331  PC Game Controller
11ff:3341  PS2 Controller
12bd:d015  Tomee SNES USB Controller
1345:3008  NYKO CORE
146b:0d01  Revolution Pro Controller
14d8:6208  HitBox (PS3/PC) Analog Mode
14d8:cd07  Toodles 2008 Chimp PC/PS3
1532:0401  Razer Panthera (PS4)
1532:0402  Razer Panthera (PS3)
1532:0900  Razer Serval
1532:0a03  Razer Wildcat
1532:1000  Razer RAIJU
1689:fd00  Razer Onza Tournament Edition
1689:fd01  Razer Onza Classic Edition
1689:fe00  Razer Sabertooth
16c0:0487  Serial/Keyboard/Mouse/Joystick
16c0:05e1  Xin-Mo Xin-Mo Dual Arcade
1949:0402  Amazon Fire Game Controller
1949:0402  Ipega PG-9069 - Bluetooth Gamepad
1a34:0809  SL-6566
1a34:0836  PS3 Controller
1a34:f705  GameCube {HuiJia USB box}
1bad:f016  Mad Catz Xbox 360 Controller
1bad:f02e  Mad Catz Fightpad SFxT
1bad:f038  Street Fighter IV FightStick TE
1bad:f501  Hori Pad EX Turbo 2
1c59:0023  Retro Games LTD THEC64 Joystick
1c59:0024  Retro Games LTD THEC64 MS Joystick
1d57:0021  Retro Games The64 Joystick Prototype
1d59:0022  Retro Games The64 Joystick Prototype
2002:9000  8Bitdo NES30 Pro
20bc:5500  GameSir G3w
20bc:5500  ShanWan PS3/PC Wired GamePad
20d6:0dad  Moga Pro
20d6:6271  Moga Pro 2 HID
20d6:89e5  Moga 2 HID
20d6:ca6d  PowerA Pro Ex
20e8:5860  Cideko AK08b
22ba:1020  Jess Technology USB Game Controller
24c6:5300  PowerA
24c6:543a  PowerA 1428124-01
24c6:5b02  Thrustmaster GPX Gamepad
24c6:5d04  Razer Sabertooth
2563:0523  ShanWan USB Gamepad
2563:0575  SHANWAN PS3/PC Gamepad
25f0:83c1  Goodbetterbest Ltd USB Controller
25f0:c121  ShanWan Gioteck PS3 Wired Controller
2717:3144  XiaoMi Game Controller
2810:0009  8Bitdo SFC30 GamePad
2836:0001  OUYA Game Controller
289b:0003  raphnet.net 4nes4snes v1.5
28de:1102  Steam Controller
28de:1105  Steam Controller
28de:1106  Steam Controller
28de:1142  Steam Controller
28de:11fc  Steam Controller
28de:11ff  Steam Virtual Gamepad
28de:1201  Steam Controller
28de:1202  Steam Controller
2dc8:2830  8Bitdo SFC30 GamePad
2dc8:3810  8Bitdo FC30 Pro
2dc8:3820  8Bitdo NES30 Pro
2dc8:6100  8Bitdo SF30 Pro
2dc8:9001  8Bitdo NES30 Pro 8Bitdo NES30 Pro
3820:0009  8Bitdo NES30 Pro
4c50:5453  PS3 Controller
5347:6d61  GameStop Gamepad
5347:6d61  GS gamepad
6258:3320  Xbox 360 Wireless Controller
6258:4720  Xbox Gamepad (userspace driver)
6469:6469  idroid:con
6666:0667  boom PSX to PC Converter
6666:8804  Super Joy Box 5 Pro
dead:beef  Hidromancer Game Controller
f000:0003  RetroPad
f000:00f1  Super RetroPort