Network, network, network!
Build a network of contacts in your area of expertise. Most major cities have a plethora of networking groups. Just do a LinkedIn or Google search to find out what is available in your area. Attend the live networking events to get people to know and trust you. By gaining their trust, they will be more likely to recommend you for an unlisted opening.
Participate in the social boards on LinkedIn. If you can use your expertise to help others solve a business problem then someone in that group may remember you if an appropriate opening comes along. Also, join and participate in appropriate forums. For example, if you are a female in the executive space then a women's leadership forum would be an excellent choice.
If you are interested in working for a particular company, find out who you know who works there, or who has someone in their network who works there and would be willing to make the connection for you. Don't be afraid to ask for a referral!
Increase your online presence and build your personal brand
Create a website or blog that highlights your expertise and why you are so uniquely awesome that any company would be better off with you on their team. Include the website on your LinkedIn profile.
Make sure your LinkedIn profile is complete and is full of keywords so that your profile will pull when recruiters search for people with your skills.
Take a course in search engine optimization (SEO) so that you will be listed in a higher ranking in search engine results.
Have you been interviewed or hired for an unlisted job opening? How did you find out about the opportunity?