Eight-bit videogames and computers have a hardware memory limit of 64K. For the Nintendo Entertainment System, only 40K of that could be on the cartridge as ROM. To get around this, they had to put extra chips on the cartridge to allow banks of ROMs to be swapped with each other. Some more advanced NES cartridges got to hundreds of kilobytes. From the programmer's point of view, all this memory swapping is cumbersome, but it is transparent to the users.
Many 8-bit computers had this capability to begin with. The Commodore 64 had 64K RAM plus 20K of ROM, making a total of 84K. The Timex-Sinclair 2068 had 24K of ROM and 48K RAM for a total of 72K. The Commodore 128, the Apple IIc, and the Sinclair Spectrum 128 all had 128K of RAM plus ROMs.
The Atari 2600 had a memory limit of only 4K, and it took bank switching with extra chips on the cartridges to go over this limit.
Sixteen-bit computers usually have a memory limit of 16 megabytes, although depending upon the hardware it could be less.
Thirtytwo-bit computers usually have a memory limit of 4 gigabytes.
In theory, 64-bit computers can get up to 16 billion gigabytes, although I would like to see somebody try. You could probably heat your home or a large building with that much memory.
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