There are lots of good cycling quotations, although the most famous one, "A woman needs a man, like a fish needs a bicycle" (Gloria Steinhem - although she attributes the quote to an Australian woman named Irina Dunn) actually has nothing to do with cycling.
Here are some of my favourites:
"Human progress should have stopped with the bicycle."~ Elizabeth West
"I lose the sense of balance, to the point Gaston Plaud and the mechanic had to support me for more than 200 meters before I could start again. Finding my way, I had to climb the thread of my own existence to know who I was, and what I was doing on the bicycle. Then I saw the 'Peugeot' on my jersey and I remembered that I was a cyclist. But in what race were we? I didn't have any idea, until I noticed the Tour's yellow plate screwed on the bumper of the Peugeot team car. Not being sure of anything, I am inquiring from Gaston Plaud who answered, 'Yes, we are in the Tour, don't worry, you fell on your head."
~ Bernard Thevenet, 1972 Tour de France, after a crash
"The bicycle is a curious vehicle. It's passenger is its engine."
~ John Howard, U.S. Olympic cyclist
"Bicycling is a big part of the future. It has to be. There is something wrong with a society that drives a car to work out in a gym."
~ Bill Nye
"The bicycle should always be the vehicle of novelists and poets."
- Christopher Morley
(P.S. Along with being a cyclist, I'm a would-be novelist)
"Those who wish to control their own lives and move beyond existence as mere clients and consumers- those people ride a bike."
~ Wolfgang Sachs, For the Love of the Automobile
And this one shows up on the internet as a "Zen Proverb." God knows where it really comes from, but even anonymous it's a good one:
A Zen teacher saw five of his students returning from the market, riding their bicycles. When they arrived at the monastery and had dismounted, the teacher asked the students, "Why are you riding your bicycles?"
The first student replied, "The bicycle is carrying the sack of potatoes. I am glad that I do not have to carry them on my back!" The teacher praised the first student, "You are a smart boy! When you grow old, you will not walk hunched over like I do."
The second student replied, "I love to watch the trees and fields pass by as I roll down the path!" The teacher commended the second student, "Your eyes are open, and you see the world."
The third student replied, "When I ride my bicycle, I am content to chant nam myoho renge kyo." The teacher gave praise to the third student, "Your mind will roll with the ease of a newly trued wheel."
The fourth student replied, "Riding my bicycle, I live in harmony with all sentient beings." The teacher was pleased, and said to the fourth student, "You are riding on the golden path of non-harming."
The fifth student replied, "I ride my bicycle to ride my bicycle." The teacher sat at the feet of the fifth student and said, "Ahh.... I am your student!"