Edit: I modified the answer in 2022, added new data on communications with Voyager.
The sort of emergency that would require this power level is rare. You're looking at events where a remote (deep-space) spacecraft loses its orientation and can't use its high-gain antenna.
For Voyager 2, communication at more than 20 kW is used routinely.
- the regular 'reset the timer, keep doing what you're doing' command is sent at 18 kW.
- if more commands have to be sent, they transmit at 75 kW(as of 2017).
The receiver on Voyager 2 has a failed capacitor which means the frequency it's tuned to is not stable. They have to find the correct frequency each time (by sending the same command at a bunch of frequencies until they get a response).
For command sequences, they want to avoid a communications session getting interrupted in the middle by this capacitor drifting, so they send at more power which gives the receiver more margin.
Older info remains here:
I found one occasion where DSS-43 was used at 95 kW: during tests for communications with Rosetta just before it entered hibernation mode in 2010:
During the hibernation entry window next year, Rosetta will be between 3.7 and 4.4 AU from Earth. At those distances, and once Rosetta is spinning, it will be necessary to be able to command Rosetta using the low-gain antenna (LGA) and to detect the strobing signal coming from the high-gain antenna (HGA).
On 19 November, a test similar to the one conducted on 20 August was repeated to validate the RF activities and performance to be expected at the end of the DSHM entry window in July 2011 at a geocentric distance of about 4.4 AU. The tested elements were as follows:
viability of LGA-F S-band telecommand link (7.8 bps) from DSN 70-metre dish (DSS-43, Canberra) with 95 kW uplink power
I haven't found other instances, but that doesn't mean it's never happened. I don't remember ever reading about an outer planetary system mission losing orientation and requiring recovery via MGA or LGA.