It's true that recruiters can now Google you as part of their search process. And tools like LinkedIn do allow you to create something similar to a resume. But you still need a resume. Here's why:
As you can see, your resume remains a key marketing document and an essential part of your job search toolkit. In fact, the work you do in preparing it will serve you well in all your job search activities, from networking to interviews and beyond.
For ideas on creating a great resume that gets results, see Resume Strategies and Do Your Research.