Since google analytic has been update, this is the new tutorial.
Step 1: Go to your google analytic account.
Step 2: Once on homepage of google analytic, click on admin on the top right.
Step 3: In your account list, select the account where your website profile is.
Step 4: In properties tab, select your website name.
Step 5: In profiles tab, select your website profile.
Step 6: click on profile settings tab in the far right and on the bottom right click on " Delete this profile "
step 7: click on "Delete profile" for confirmation.