Here's a proposed simple generator for a swept frequency square wave (as yet unbuilt).
According to LTspice it is not fussy over component values provided the time constants R1C1 and R2C2 are different.
The only uses I can presently think of for it are as a test signal generator, e.g. for determining a filter or amplifier response, or in a chirp sonar application. Any other uses you guys 'n gals can think of?