A letter of inquiry is a good way to connect with a company.
Because the letter is unsolicited, sending it shows that you're proactive, and have a genuine interest in the company. As well as inquiring about open or upcoming positions, a letter of inquiry can also be used to set up an informational interview with human resources or higher level employees.
While the company may not be hiring currently, or may not have a job posted that is appropriate for you, a letter of inquiry will help you be on the company's radar when opportunities that are suitable for you arise.