For running, I don't do a ton of warming up. I do a few stretches, but gently. I take a short walk (1/4 mile at most), and then start my run. But ... I'm not running hard. If I were, I'd do more of a warmup. Even now, if I walk (briskly) longer before I start my run, the first half mile is not nearly so unpleasant (my first half mile always makes me wonder if I only imagined I'd been running since August
) - but, I put up with it rather than make my work out longer, at least for now.
I also do yoga, which is obviously lots of stretching, and I do warm up first, by doing Sun Salutations, which are also a yoga sequence, with both muscular work and light stretching. Great warmup for early morning yoga, which is when I do it, and is a time my muscles are cold. If for some reason I do yoga in the evening, I'm noticeably more flexible, even without a warmup.
If I ever manage
to start doing a resistance workout a couple times a week (resistance bands) in the morning, I plan to use the Sun Salutations for a warmup.