I am in the "they don't weigh much, take plenty" camp.
I've cycled ~8000 miles across Europe+Asia and had one flat. Used that as an opportunity to replace worn rear tire (I had two spare tires with me) and finished rest of the trip with only that one flat.
At opposite side of ledger:
- One year on the HI-AYH San Diego Christmas ride, I got 6 flats in a day. I was unlucky, it was raining and I hadn't quite addressed the root problem.
- While touring, my largest number of flats in a day on my bike has been three. I have however, cycled with a partner where I fixed 5-6 flats on their bike.
Hence, as a result, I often end up with two or three patch kits, at least two tubes - and sometimes a spare pump. Overkill, but it has kept me going.