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8/64 warning

Every operating system requires

Sufficient Flash to accommodate firmware image
Sufficient RAM for stable operation

Devices with 8MB flash and/or 64MB RAM will work but they may be somewhat limited regarding installing additional packages due to low flash space and/or low RAM amount. Consider this when choosing a device to buy, or when deciding to flash OpenWrt on your device because it is listed as supported.

Usability issues

Insufficient RAM for stable operation

32 MB RAM is already deprecated. You will run into issues with an up to date OpenWrt version.
64 MB RAM may have some issues with stability, depending on your hardware and use cases, although it is enough for basic usage
128 MB RAM or more is recommended if software past basic router/AP functionality is to be used

Extensibility issues

Barely enough Flash to accommodate OpenWrt firmware image

8MB is barely enough (will fit LuCI and some other applications, but not many) / 16MB offers more flexibility
8MB devices can be extended if you use the Image Generator (Image Builder) (that requires a Linux system and some mild experience) or use Extroot. Experienced users creating custom builds may be able to save firmware space, but many packages won't ever fit no matter what you do.
If you want to be sure you can install at least a few additional software packages, 16MB (or more) of flash and 128MB (or more) of RAM are the recommended choice.

As the current stable 21.02 release uses kernel 5.4 that is roughly 0.5 MB larger than the kernel 4.14 used in the old 19.07.x releases, and SSL/HTTPS has been enabled by default needing at least some 0.3 MB flash space for the SSL libraries, the free flash space available on 8MB flash systems will be rather small in the current OpenWrt 21.02 release. OpenWrt master has already partially moved to kernel 5.10, which is still larger.

Flash space is also needed for bootloader (u-boot, etc.), bootloader settings, wifi firmware/calibration data, possible OEM settings (for ability to revert to OEM firmware) and for the jffs2/ubifs overlay space (OpenWRT config storage). Thus the maximum available flash size e.g. in a 8MB flash is actually typically 7MB or less.

Advice

Users that are not expert users of OpenWrt (those that can build their own images) should consider

16/64 as an absolute minimum for any device, with at least 128 MB of RAM being preferred.

Users should expect that devices with less than 16 MB of flash and/or 64 MB of RAM may be unstable in basic operation under OpenWrt from 21.02 onward. They should further expect that support for the device may be dropped in future.

Analysis of firmware size growth

As example, the size of the sysupgrade release image for WNDR3700v1, an ar71xx/ath79 device that has been supported by Openwrt for ten years:

main/master:   5696.3 KB (snapshot without LuCI)
23.05-rc1:     5888.3 kB
22.03.5:       5952.3 KB
21.02.5:       5312.3 KB
19.07.8:       4096.3 KB
18.06.8:       3712.0 KB
17.01.7:       3584.0 KB
15.05.1:       3584.0 KB
14.07:         3328.0 KB
12.09:         2816.0 KB

Main reason is growth in size of the Linux kernel itself, but all included core packages (wifi, LuCI, etc.) also tend to grow as their features get expanded.

More thorough discussion can be found in 4/32 warning.