According to this a "typical" omnivore cyclist produces about 3 times less carbon than a "typical" driver. Vegan and vegetarian are about 4 times less. You can play around with the numbers in the calculator. I think this guy's probably biased towards veganism, but this is what I've seen.
I haven't seen a comparison with motorcycles or electric vehicles, or a comparison that took into account the embodied energy of the vehicles.
Edit: This calculator also assumes equal trip distances between modes of transportation, which is not realistic in my experience. Cyclists tend to have shorter trips. So that's another factor to consider.
> You can’t effect the amount of carbon released by adopting a low carbon lifestyle when the price of fossil fuels is above the cost of production. All reducing demand at the margin does is lower the marginal price causing an increase in consumption elsewhere in the economy.
If that's true, then I guess the goal is to slowly reduce the price. Perhaps cycling is ineffective in terms of carbon emissions. This is okay for me as I find either the cost or physical fitness benefits convincing in isolation.