Business Registrations
If you are running a business, obtaining a domain name can be quite beneficial.
Your business can have a website, accessible from the domain name.
You can add unique email addresses @YOURDOMAINNAME.WHATEVER
You can add your domain/email to brochures, business cards, uniforms, cars etc.
This makes the promotion of your business easy, people will remember your name and be able to find you (website, yellow pages, email).
Having a domain name that reflects your business helps you look like an established business and build customer trust.

Individual/Personal Registrations
If you want to tell the world about yourself, what you are interested in, what is happening in your life, your thoughts and special events then a domain name is for you. You can add a website, email and let friends and family contact you through either. It also makes your email address unique to you.