Bare Minimum
I always bring backup equipment to a shoot - two bodies, two primes (somewhere between 28mm to 135mm) and a mid-range zoom (28-70mm or 24-120mm). Backup cards and batteries are a must as well.
While I love being prepared for all sorts of equipment failure and changing shooting conditions, I decided to do things differently on a recent portrait session.
I only brought the bare minimum of photographic gear: My Nikon D800, the Nikkor 105mm f/2 DC for headshots and the Voigtlander 40mm f/2 for full-body shots and a spare battery.
How was it then? Carrying a lighter bag was convenient, but not having my full setup to choose from, led to a feeling of anxiety. In the end, everything worked out, my Nikon never let me down so far.
However, would I recommend going out without backup equipment? No - never risk not being able to deliver ever. It ruins your reputation.
I have to admit that the shooting did not take place far away from my studio, so in case any critical equipment failure would have occurred, I would have been able to get a replacement in under 20 minutes. Otherwise I would have brought at least a Fuji X100V as a backup.