The thing I hear the most when talking to people who have never tried yoga is, "I'm not flexible enough to do yoga." What I tell them is, you don't have to be flexible!
There is a quote floating around on the internet that goes, "Yoga is not about touching your toes. It is what you learn on the way down." Although I could not quite find exactly who said it (some sources credit Dr. Jigar Gor while others attribute it to Dr. Judith Hanson Lasater) I love this quote, because although you may gain flexibility through your practice, yoga is not about being flexible. The practice of yoga goes beyond what you see in gyms, classes, and television shows. What you can see is one small part of the practice of yoga called asana or the postures.
When I began taking yoga classes over 15 years ago, it was at a local gym and I thought it would be a good workout. I was not flexible when I began yoga. My strength, flexibility, and body have changed quite a bit in this time. In my 20's I was interested in strong, powerful, sweaty classes. Now, in my 40's I tend toward slower paced classes with deeper holds in asana. Through my practice I have changed and grown in so many ways beyond what can be physically seen. Yoga has help me gain more awareness of myself and the world around me. Sure, I have gained some flexibility in my physical body since starting my practice. I have also learned that there are some ways in which my body will never be flexible, and that's okay! Most importantly, I have learned so much about myself, my body, and my mind along the way.
Please don't let the idea that you have to be flexible keep you from trying yoga! Keep in mind that there are many different types of yoga and many different teachers out there. You might have to "shop around" a bit to find a class and a teacher that fits your needs. A good teacher will listen to your goals and help to guide you to the type of class or teacher that is right for you, so don't be afraid to ask!