Yes, pure quinoa is gluten-free, making it safe for people with celiac disease and gluten intolerance or gluten sensitivity. However, that doesn't mean that all products containing quinoa are gluten-free in fact, some are not.
Quinoa isn't really a grain it's the seed of a plant that's related to spinach, not to wheat. Therefore, if you can find plain quinoa whole or flour that's labeled or certified gluten-free, it makes a perfect substitute for grain-based menu items. I've used it as whole-"grain" hot cereal (cook it as you would oatmeal), and ground into flour for flatbread.
Quinoa also makes decent pasta and a good base for cold cereal. I've seen it used in cold summer "grain"-based salads instead of bulgur wheat, and even in gluten-free flour blends for cakes and pastries.
Many but not all of the quinoa-based products on the market are considered gluten-free.
For example, Ancient Harvest makes a variety of safe quinoa products, including pasta that's based on quinoa and corn flours and made in a gluten-free facility. Orgran, another manufacturer of gluten-free products, makes gluten-free cereal, flatbread and multigrain crumbs with quinoa.
Bob's Red Mill makes quinoa flour in a gluten-free facility (although celiacs who can't tolerate oats should know that Bob's also processes its gluten-free oats in that facility). However, Bob's Red Mill also makes an organic 7-Grain Pancake Mix with quinoa ... and that mix is not gluten-free.
The bottom line is, you can't assume that products containing quinoa as their main ingredient are gluten-free, just as you can't assume products that contain rice or corn as their main ingredient are gluten-free. You always have to check the ingredient label for terms that mean gluten before buying anything.