I imagine that many members of this forum (especially those who work on emulators) know what I'm talking about here; by such terms as "8-bit" and "64-bit" is meant the word size of the CPU and nothing else: Even if a computer cannot take in 64 bits at a time (for example, the N64 with its 32-bit data bus), if the largest unit of data it can work with in one operation is 64 bits then it is a 64-bit machine.
In particular, the CPU word size (a.k.a. "bit-rating") says nothing about the CPU speed, number of cores, amount of memory, or graphics processing power, though up to the fifth generation of video games, increases in CPU word size did indeed go along with more general increases in the power of the video game systems, and that is why you saw things like "16-BIT" in relief on the original Genesis console and such names as the TurboGrafx-16 and Nintendo 64, while you don't hear much about this stuff now because we don't exactly have 256-bit consoles even though that's what a lot of us expected two generations out from the days of the N64!
Anyway, I thought this would be a good place to collect some information about the CPU word sizes of various consoles and handhelds (BTW, the last *handheld* to be marketed by its CPU word size was the 32-bit GBA IIRC, and then only briefly) and maybe even arcade machines throughout history; I imagine that someone else has done it on the Internet, but I don't know where, even though I believe all the necessary information is available on Wikipedia.
N.B.: Before you laugh at the first entry in this skeleton, I do know at least that the first Texas Instruments calculator was 4-bit, using the Intel 4004.
Fake edit: Well what do you know, the first handheld ever (Microvision) was 4-bit.
*THIS LIST IS INCOMPLETE, ESPECIALLY THE ARCADE MACHINES!*
4-bit
Handheld:
Milton Bradley Microvision (later TI TMS1100 version)
Console:
Arcade:
8-bit
Handheld:
Milton Bradley Microvision (original Intel 8021 version)
Sony Playblock
TimeTop GameKing
Tiger game.com (Sharp SM8521)
Watara Supervision (Western Design Center 65C02)
several companies Mega Duck/Cougar Boy (MOS version of the Z80)
Pelican VG Pocket Tablet
Nintendo Game Boy, Game Boy Color (custom Sharp x80s, implemented a subset of Z80 functionality)
Sega Game Gear (Zilog Z80)
Sega Dreamcast VMU (Sanyo LC8670 "Potato")
Atari Lynx (MOS 65SC02 with 16-bit address space, also contained custom 16-bit CMOS graphics chip "Suzy")
Console:
Atari 2600, 5200, 7800 (based on MOS 6502)
ColecoVision (Z80)
Emerson Arcadia 2001 (Signetics 2650A)
Fairchild Channel F (first system to use ROM cartridges and first to use a general-purpose CPU and therefore have a "bit-rating"; used the Fairchild F8, made by Robert Noyce, who would later found Intel)
Interton VC 4000 (Signetics 2650A)
Magnavox Odyssey² (Intel 8048)
Sega SG-1000, SC-3000, SF-7000, Master System (Z80 or clone)
Nintendo Entertainment System (Ricoh 2A03)
NEC TurboGrafx-16 (modified 65SC02, with two 16-bit GPUs)
Uzebox (ATmega644)
Arcade:
Namco Pac-Man, Galaga, Pole Position (Z80)
Nintendo Radar Scope, Donkey Kong, PlayChoice-10 (Z80)
Nintendo Vs. UniSystem, Vs. DualSystem
Midway Astrocade (Z80)
Sega G80, System 1 (Z80)
16-bit
Handheld:
Pelican VG Pocket Caplet
SNK Neo-Geo Pocket Color (Toshiba TLCS900H, with Z80 for sound)
Bandai WonderSwan, WonderSwan Color (NEC V30MZ or clone)
Console:
Mattel Intellivision (GI CP 1610)
GCE Vectrex (Motorola 6809)
Nintendo Super Nintendo Entertainment System (Ricoh 5A22)
Arcade:
Namco Libble Rabble, Super Pac-Man, System 86, System 1 (Motorola 6809)
Nintendo Super System (Ricoh 5A22)
32-bit
Handheld:
Nintendo Virtual Boy (NEC V810)
Nintendo Game Boy Advance (ARM7TDMI)
Nintendo DS and DSi (ARM946E-S and ARM7TDMI)
Nintendo 3DS and New 3DS (ARM11)
Sony PocketStation (ARM7T)
Sony PlayStation Vita (ARM Cortex-A9 MPCore)
Cybiko Classic, Extreme (Hitachi H8S)
Shanda EZ Mini (PXA270)
Game Park GP32 (ARM920T core)
Game Park GP2X, XGP (ARM920T and ARM940T)
Nokia N-Gage (ARM9E)
Tapwave Zodiac (Motorola i.MX1 ARM9)
Tiger Telematics Gizmondo (ARM9)
Console:
Nintendo 64DD
Nintendo GameCube (IBM PowerPC Gekko)
Nintendo Wii (IBM PowerPC-based "Broadway")
Nintendo Wii U (IBM PowerPC "Espresso")
Sega Genesis (Motorola 68000 with a 16-bit data bus, and a Z80 for sound and SMS compatibility)
Sega CD (faster Motorola 68k with 16-bit bus)
Sega 32X, Saturn (2 Hitachi SH-2 RISC)
Sega Dreamcast (Hitachi SH-4 RISC with some 128-bit FPU operations)
SNK Neo Geo AES, Neo Geo CD (Motorola 68k with 16-bit bus)
Philips CD-i (Philips 68070, based on Motorola 68k, with 16-bit data bus)
Commodore Amiga CD32 (Motorola 68020)
Atari Jaguar (Motorola 68k with 16-bit bus, with a 32-bit "Tom" GPU with some 64-bit instructions and a 32-bit "Jerry" DSP chip)
3DO (ARM60)
NEC PC-FX (NEC V810)
Sony PlayStation (MIPS R300A)
Microsoft Xbox (custom Intel Mobile Celeron, based on the Pentium III)
Ouya (NVIDIA Tegra 3, similar to ARM Cortex-A9)
Arcade:
Namco System 2, System 21, NA-1, ND-1 (Motorola 68k with 16-bit bus)
Namco NB-1 (Motorola 68020)
Namco System 22, System Super 22 (Motorola 68EC020)
Namco System 11, System 12 (MIPS R3000A)
Taito F3 System (Motorola 68EC020)
Taito Type X, Type X+, Type X7 (Intel Celeron)
Taito Type X² (Intel Celeron D, Pentium 4, or Core 2 Duo)
Capcom Play System, Play System 2 (Motorola 68k with 16-bit bus)
Capcom Play System 3 (Hitachi SH-2 RISC)
SNK Neo-Geo MVS (Motorola 68k with 16-bit bus)
Midway T Unit (TI TMS34010)
Sega System 16, X Board, Y Board, System 18, System 24, Mega-Tech, Mega-Play, System C-2 (Motorola 68k with 16-bit bus)
Sega System 32, Model 1 (NEC V60, with 16-bit data bus and 24-bit address bus)
Sega Model 2 (Intel i960)
Sega ST-V (2 Hitachi SH-2 RISC)
Sega Model 3 (IBM PowerPC 603)
Sega NAOMI, NAOMI 2 (Hitachi SH-4 RISC with some 128-bit FPU operations)
Sega Chihiro (custom Intel Mobile Celeron, based on the Pentium III)
Sega Lindbergh (Intel Pentium 4)
Nintendo/Sega/Namco Triforce (IBM PowerPC Gekko)
64-bit
Handheld:
Sony PlayStation Portable (based on MIPS R-4000)
Nintendo Switch (ARM Cortex-A57 and ARM Cortex-A53)
Console:
Nintendo 64 (NEC VR4300 with 32-bit data bus, and a 64-bit SGI GPU)
Sony PlayStation 3 (Cell Broadband Engine)
Sony PlayStation 4 (AMD Jaguar)
Microsoft Xbox One (AMD Jaguar)
Arcade:
SNK Hyper Neo Geo 64 (RISC)
Namco System 23, System Super 23 (MIPS R4650)
Sammy AtomisWave (Hitachi SH-4 64-bit RISC)
128-bit
Handheld:
Console:
Sony PlayStation 2 ("Emotion Engine")
Microsoft Xbox 360 (IBM PowerPC Xenon triple-core)
Arcade:
Namco System 246, System 256, System Super 256 ("Emotion Engine")
*THIS LIST IS INCOMPLETE, ESPECIALLY THE ARCADE MACHINES!*
I decided not to include systems consisting of a repackaging of the same basic hardware, like the Nomad (portable Genesis), TurboExpress (portable TurboGrafx-16) or SwanCrystal (WonderSwan Color with a prettier LCD screen). Also, some peripherals, like the Famicom Disk System, did not have CPUs of their own as far as I could tell.
Additionally, it seems as if none of the first-generation systems had general-purpose CPUs, and instead either used "game on a chip" designs or discrete circuitry; also, during the era of the first console ever (the Magnavox Odyssey, which used jumper cartridges with no ROM at all), the designer (Ralph Baer) had an idea that, if it had caught on enough to seem patentable, could have meant a financial death knell to nearly all ROM cartridge systems that came later on in the second generation and prevented such marvels as the DS and SNES from ever existing.
I should mention that this topic will become controversial for the simple reason that I listed the TurboGrafx-16 as an 8-bit system and the Genesis as 32-bit...but for the latter issue, I had to be consistent here: The Genesis used a 32-bit Motorola 68k with a 16-bit bus and the N64 used a low-end 64-bit MIPS CPU with a 32-bit bus, and the Genesis always used 16-bit operations and the N64 almost always used 32-bit operations (which is why you can emulate it on 32-bit PCs lol).
Perhaps I should list the Genesis as 16-bit and the N64 as 32-bit? Then again, word size != data-bus size...
Also, as far as I can tell, all the add-on chips included in various SNES cartridges are 16-bit, except that the Cx4 chip in Mega Man X2 and X3 might be 24-bit, but I'm not sure if that's the right way to interpret the phrase "triple-byte registers":
http://users.tpg.com.au/advlink/dsp/cx4.html
Fun Facts: The Z80 and ARM processors are used in several graphing calculators, the Motorola 68k was used in Macs until System 7, and PowerPC CPUs were used in Macs after that until a couple years ago!
Now, I wonder what CPUs the Nintendo Game & Watch units used...