Paypal Express No Button
Two settings that can cause this issue are:


The link to the button image is missing in the payment processor settings. The setting is called "Button URL" and it should normally point to https://www.paypal.com/en_US/i/btn/btn_xpressCheckout.gif.
The page is configured for membership signups and has the option turned on to allow "Separate Membership Payment" in the contribution page's membership tab. This setting is currently incompatible with Paypal Express. In some versions of CiviCRM this setting causes the Paypal Express button to be hidden. In others an explicit error is given when clicking on the button. See: https://issues.civicrm.org/jira/browse/CRM-8221