I was just setting off to go to York one weekend last June. There was a steady parade of cyclists coming up the hill towards me - it was the weekend of the CTC rally and this was a challenge ride route.
Just outside the village was a guy fiddling with his rear tyre. I asked if he was OK. He asked if I had a pump; I had. Turned out he'd used all his CO2 cartridges up, but kept finding more punctures. I didn't have a tube to fit his skinny rims, though. By the time he'd fixed the punctures and pumped his tyre back up, he'd decided to abandon the ride and head back to York.
But hey, he was riding, not walking.
A little further down the hill was another guy standing by an upside down bike. Did he need any help? Yes - his rim had split. Now, funnily enough, I had a wheel in my trailer (on its way to York Bike Rescue...) - but it was a wobbly 27", and the guy had a mate on his way with a car.
Next year, I'm thinking of lurking on the same route with a trailer full of spares and a colllection box for my favourite Charidee.
I've had my share of folk offering to help, usually when I didn't need it, and whizzing blithely by, looking studiously the other way when I did.
It never hurts to ask if someone wants a hand.