Is it better to adopt a cat from a no-kill shelter? And do such shelters really not euthanize any of their animals?
While laws vary per state, "no-kill" generally means that all adoptable and treatable animals will not be euthanized. Unfortunately, many of these shelters do not accept all animals in the first place. For example, a feral cat that once wandered into my garden had kittens. I worked to socialize both the mother and the kittens for a few weeks, but a local no-kill shelter still felt they were not adoptable, so they were rejected.
According to The Hayden Law in California, "adoptable" is defined as "only those animals eight weeks of age or older that at or subsequent to the time the animal is impounded or otherwise taken into possession have manifested no sign of a behavioral or temperamental defect that could pose a health or safety risk or otherwise make the animal unsuitable for placement as a pet." It goes on to address health concerns.
You will find loving animals in need of homes at all shelters. If a good no-kill shelter happens to be near you, I encourage you to visit it. The Humane Society of the United States estimates that shelters euthanize three to four million cats and dogs each year, so you could very well be helping to reduce this overwhelming number.