Can anyone tell me when XLR connections were first used on stereo equipment. (what years)?

I have a Burmester 838 phono preamp and an 868 preamp/DA convertor and two 878 amps, all of which have XLR connections.  Burmester used a system to identify his components : 838 [ August of 1983 ] 868 [August of 1986 ] 878 [August of 1987]. Year followed by month.  So, I guess my earliest guess would be 1983 that Dieter started using XLR connections.  Incidentally, his were 4 pin XLRs --- the 4th pin being used to "trigger" the on/off function if desired.  His adoption of "balanced technology" is credited to 1983.  I think I've got this right.

Levinson ML-26 has balanced pre-out and optional XLR instead of phono card. 

Note that there is a difference between XLR connection and balanced operation.  Much of the benefit of XLR connectors arises from being used with a balanced circuit,.  However, as Ralph mentions above, there are plenty of ways of having balanced in/out connections without using balanced circuitry throughout the device.

If you're shopping mid-fi, there's an increased chance of running into devices using XLR into a not-truly-balanced circuit.  I'm guessing that all of the brands mentioned above are fully balanced, but defer to @atmasphere

PS I believe some Threshold preamps & amps had XLR connections in the 80s and 90s, but I don't think they ever made an integrated amp.  Much more recently, Parasound HINT & HINT 6 integrated amps include XLR ins & outs.  I don't know if any of them are truly balanced, but both companies were/are highly reputable.

Note that most consumer gear with XLRs only support 1 balanced input/output, as balanced consumer gear is rare.  Someone with a good knowledge of pro gear might be able to steer you to some other alternatives.