Many of us go straight from our workouts to our errands, so wearing clothes that can literally move with us as we live is not only convenient, but often a necessity. I am not willing to go out to lunch in sweats, nor go to my workout class in jeans, so I found two places that agree with both my my principal of versatility and my sense of style.
The first store is Lucy, which has stores all over the U.S., as well as a website with soft, stylish, comfortable outfits and separates in neutral palettes. I can wear their everyday pants (which have POCKETS!) out at night with a sexy tank top after wearing exactly the same outfit doing Pilates. I love that their clothes are all machine washable; they offer short, medium, and tall pant sizes, so you don't have to hem! If you sign up to be on their mailing list online or in a store, they will send you coupons that you can print out or use online for discounts of up to 50% off regular and / or sale merchandise.
The second store is Lululemon from Canada. Their clothes are pricey, but the feel of their fabrics has a "soft hand" feel that belies quality. They have flat seams on their pants so you never feel an edge while doing floor exercises. Think of justifying the price by buying one pair that you love and will wear instead of buying two pairs of pants you sort of like but won't wear. The real price is always calculated based on whether you will actually use what you buy.
They have a huge selection of sports bras to fit every activity and every chest in a rainbow of colors, and they will hem your pants for you in most stores for a small fee. They have stores in most big cities or you can shop online. Every once in a while they have sale items from past seasons and styles, so if you want to save some money, choose something from their sales rack.
Of course another great way to shop for workout clothes that work out in the world is to check on Ebay for the same brands you love in the stores; just make sure that the sellers have 1) at least a 95% positive feedback rating (I always read the negatives even if they only have a few) and 2) they have enough transactions to make the ratings count (at least 100 ratings).
Once you get used to being in comfortable clothes that work everywhere you go, you will never settle for anything less. And you shouldn't.