I do Ashtanga yoga on the alternate days to my weight training. My yoga instructor would rather have me do it every day (Mysore style), but I find it's too exhausting to both lift and do my yoga practice on the same day. (Yoga here is also rather expensive, so it's cheaper for me to do it at a daily class rate than to get the monthly membership at my studio.)
I do Ashtanga because it's intense but controlled. My progression is closely monitored by my instructor (who has trained extensively in Mysore, India) and it's not an "athletic" form. I don't know how people can do that "hot" style yoga. I sweat enough for two people when I exercise; I'd be soaked to the bone if I did yoga in a hot room!
My personal trainer is also not a huge fan of doing a lot of stretching. He's an exercise physiology researcher at Tufts University here in Boston, and he has tomes of research that says too much stretching can be counterproductive for anyone who is serious about strength training. But then he's also not a fan of my vegan diet, so I take his advice in moderation