Certain professions will lend themselves to getting cold called by headhunters: consulting, finance, maybe law(?), and others. I would imagine it's pretty rare to get headhunters calling on you if you're not in one of those industries. Those professions are known for a) high turnover, b) lots of people looking for placement in other industries, and c) skill sets that are generally transferable to a wide range of jobs and industries.
If you're not in an industry/function where headhunters will reach out to you, you'll want to reach out to them. Chat with some that come recommended by friends. Afterward, send them your resume and ask for honest feedback about placement prospects. If they're good, they will be honest with you and will also give you constructive feedback. If they want to work with you, they'll let you know. If they don't, don't push them. The better headhunters will be more discerning with whom they take on as clients. In fact, it's sometimes a bad sign if a headhunter is willing to take just anybody. Never trust someone who will take you on with no questions asked.