Of course. There is a growing number of companies that will happily look at LinkedIn and personal websites, but the vast majority of companies have HR employees that will insist on a CV in Word or PDF format for an interview.

I'm currently in the process of interviewing for a new job. If there's an option to import my Linkedin data, I'll do that. Otherwise I'll send links to my personal site, Github, and Linkedin. If someone specifically asks for a resume or C.V., I'll politely say that I don't have an up to date version and to please refer to my public Linkedin page. I have not noticed had any negative consequences from not having a CV or resume.

(Disclaimer: I'm not a developer.)

I still use a resume. In my opinion, if I were hiring a developer, if the person doesn't spend the minimal effort of sending an updated resume, it shows lack of interest on his part. Providing additional links would be a great supplement, but I can't see that as a pure replacement.

A lot of (larger) companies use tools like Resumator which require a pdf/doc CV in order to upload an applicants details. Personally I don't mind referring to linkedin for a candidates background provided they have a github/bitbucket account that lets me see beyond their work history.

It really matters what field you are in. The more traditional fields will absolutely need a Resume/CV.