Importance of Undergraduate Research
If you want admission to the very best PhD programs in the US, prior formal research experience is very important, if not necessary.  Admissions committees are primarily looking for evidence of research potential.  The best possible evidence for "I'll be a good researcher someday" is "Look, I'm already a good researcher."  So having formal peer-reviewed publications is better than having publishable but unpublished results, which is better than having research experience but no publishable results, which is better than having no research experience.  If you're applying to the top PhD programs, you will be competing with applicants (yes, plural) who have peer-reviewed publications (yes, plural).