OK, all flight controllers, I'm going around the horn
Are there any recorded instances of a No-Go?
One thing to note is that these polls of the room are largely for-the-record - in other words, if a flight controller was sitting on a problem that would prevent the accomplishment of a major milestone, and didn't tell Flight about it until the poll, that flight controller would not be in MCC for their next shift.
That said, and apologies because it's anecdotal, I've heard it at least once on the loops myself.
During the first attempt to launch STS-088, when Ascent/Entry Flight Director John Shannon polled for a go for launch, Weather (the controller position) was "no-go, forecast no-go" (meaning that current conditions were outside of flight rules, and were not forecast to improve by the launch time)1. Despite this, Flight reported to the Launch Director at KSC that Houston was go for launch. The Weather guy couldn't believe what he was hearing and requested clarification from Flight on the loops, and was shot down.
That was a weird launch attempt for several reasons and I'm kinda glad it got scrubbed. The next day everyone was on their A game and it went off fine.
1This wasn't news to Flight, it had been reported to him previously.
I don't think Weather being no-go for launch is particularly novel; this just happens to be one that I was there for.
The No GO happens all the time. Many recent ULA and Spacex Launches get a NO GO - Most of the time its the Weather and the Range Telemetry guys. High Altitude winds , Range tracking failures , data drops etc. If you watch Spaceflightnow or any of the launch scheduling websites you see launch halts in the last 4 or 30 minute hold all the time, then the launch usually goes fine after a day or two delay
Apollo 11 had a conditional "Go" from flight during the "1202 alarm" discussions.
Armstrong: Give us a reading on the twelve-oh-two program alarm, Mission Control.
Flight: We’re go on that flight
Kranz: We’re go on that alarm?
Flight: If it doesn’t reoccur, we will be go
CAPCOM: Roger. We got – we’re go on that alarm
Aldrin: We got good data
As Mr Marble points out in the other answer, these round-the-horns are the final confirmation checks before major mission events and are the culmination of extended periods of discussions checks, and re-checks. Any No-Go decision would and should have been discussed and resolved before this final round of confirmation.