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Running Drupal on a shared hosting environment could become a challenge when the site starts getting a lot of visitors. So f you run your Drupal installation on one of the shared hosting providers like GoDaddy, Hostgator, Dreamhost etc and your site is reasonably popular then it is likely that you would have run into performance issues if the site is not configured correctly. If you configure your Drupal site correctly you should be able to stick with shared hosting for a longer period of time before moving on to dedicated hosting.