Rarely. Nearly all neck stiffness is minor, diffuse musculoskeletal pain: several mildly irritated structures adding up to uncomfortable, reluctant movement as opposed to physically limited movement. The most common scary neck stiffness is the “nuchal rigidity” of meningitis — which makes it very difficult and uncomfortable to tilt the head forward — but that will be accompanied by other serious warning signs, of course. Like feeling gross otherwise (flu-like malaise).
I am a science writer, former massage therapist, and I was the assistant editor at ScienceBasedMedicine.org for several years. I have had my share of injuries and pain challenges as a runner and ultimate player. My wife and I live in downtown Vancouver, Canada. See my full bio and qualifications, or my blog, Writerly. You might run into me on Facebook or Twitter.