Short answer is YES they are still important. However considering the short amount of time a hiring manager will review the letter and resume, it is increasingly important that the cover letter be well written and a quick visual narrative to show the reader why YOU are the best fit.
So what do you want in your cover letter and what format? The critical piece here is showing the reader how you are the best match for what they are looking for. The T-Style or T-Letter format is a really user friendly way of achieving this.
Here is an example:
Dear Human Resources:
(Opening paragraph about what interests you about the role/company)I have been a long time user of ACME products and I am very interested in the Project Manager role., recently advertised on your company website. Having related project management experience in the consumer goods industry makes me a qualified candidate for your needs. Your Needs My Qualifications
Five years of PM experience Seven years of PM experience
Consumer Goods Industry Exp. Four years Industry Exp.
PMP Certification PMP Certification
Customer Relations Main POC for customers
(Their requirements and how you match - two lists, can be bulleted)
Awarded Top Customer Service within Project Management three years in a row .
I have attached my resume for your review. I am confident you will find my background and experience an excellent match for the talents you are seeking. I have spearheaded many solutions within my project management career that have helped to increase efficiencies and customer satisfaction. (Closing paragraph - good to include a line or two about the value you could bring to the role or pain point you have solved)
I welcome the opportunity to speak with you in person about my qualifications and the value I can bring to ACME. I look forward to your response.
Thank you for your consideration. _____________________________________________________________________
The key here is to paint a quick picture for the reader that connects the dots. If the application is via email, then by all means have your cover letter be the body text of your email and then just attach your resume. If you have difficulty with formatting the T part, just bullet each list beneath each other.
Given the very short amount of time a Hiring Manager or Recruiter has to comb through all their applicants, a Cover Letter helps highlight your specific skills and the way they match up, potentially differentiating you and giving you a greater chance of making it to the next step.