Biggest tire that will fit properly, preferrably a light casing from Panaracer. These are labelled Compass Rene Herse, Rivendell, and other brands.

On my Zero Bike, I have room for 35's without fenders. Since that bike resides in the People's Republic of Berkeley, it doesn't have fenders. Pic from last year's TdMIL, by calender almost one year ago, but feels like ten:



My purpose built gravel bike has Rat Trap Pass tires, which are insanely wide (54mm).



On vintage frames you generally have larger clearances for wider tires. Generally speaking the older the frame, the larger the clearances. Somewhere in the 70's the trend towards shorter chainstays and fork blades started. I've found that some frames can't fit 35's. I have one bike with 32's, but can really feel the difference due to smaller volume. Enter the Jack Brown's, measuring 33 1/3, sold by Rivendell. The weight is both claimed and weighed personally by me to be almost exactly between the Rene Herse 32's and 35's. The casing looks exactly the same. The tread is different, but I'm of the opinion that this is such a minor difference that only a person with the initials Jan Heine could notice. I have these on a couple of bikes.

Grander Sportier:


Pimp Eroica Grand Sport:



The Jack Browns are truly Goldilock tires. The ride difference between 32's and 33 1/3 is definitely perceptible.