How do I check busybox version (from busybox)?

Invoke the busybox binary as busybox, and you get a line with the Busybox version, a few more lines of fluff, and the list of utilities included in the binary.

busybox | head -1

Most utilities show a usage message if you call them with --help, with the version number in the first line.

ls --help 2>&1 | head -1

You can check the version on any system running busybox by running any of the commands with the --help flag to see usage. The first line of the usage calls includes a note about the busybox version:

$ cat --help
BusyBox v1.18.4 (2011-03-13 15:36:03 CET) multi-call binary.

Usage: cat [FILE]...

Concatenate FILEs and print them to stdout

If you are not running busybox but have it installed on your system, you can check by instantiating one of the utilities like so:

$ busybox cat --help

(Edit: As Gilles notes you can also call the busybox binary without a command and get the same header)

Lastly, there is also a note at the end of the man page that shows what version it's from:

$ man busybox | tail -n 1
version 1.18.4    2011-03-13     BUSYBOX(1)