Most vacancies, particularly in the private sector, are never advertised. They are filled by people already known to the employer or known to a contact of the employer. So of course it is worthwhile making yourself known. There is no reason why you should not contact an employer to ask about jobs available. If an employer can fill a job without advertising, it saves them time and expense. Even if they don’t have vacancies now and you make the right impression, they may contact you in the future.
Find out as much as you can about the organization before you approach them. Identify a suitable senior manager or professional and address your letter to them. Look for someone in a position of influence but outside HR. Then tailor your letter carefully to show your interest in the organization, tell them why you would like to work for them and how what you have to offer might meet their needs. Ask for an opportunity to talk to them to learn more about the organization and future opportunities. Offer to send your CV. Keep you letter simple, straight forward, polite and on one sheet. Check it very carefully for accuracy and typos.
Many people try to find out the name of person responsible for hiring new staff and write to them. But a direct approach to a senior executive in the department you want to work in is often more successful. If you have done your homework and show a real interest in the company you can find this direct contact can be a very good way in.