When records are accessible by the System Administrator but not standard users, there could be more than a single reason for this. Typically, the access to these records is denied because the configuration of the Organization-Wide Defaults (OWD)
If the OWD for the records in question, for example Leads is set to Private, only the System Administrator, the record owner and users above the owner in the role hierarchy will be able to see these records.
You might need to change the OWD value for this object to something less restrictive, like Public Read-Only, or create sharing rules to open up access to these records.
For more information about OWD, Role Hierarchy and Sharing rules, visit the following Help & Training articles.
About Organization-Wide Sharing Defaults: https://help.salesforce.com/apex/HTViewHelpDoc?id=security_sharing_owd_about.htm&language=en_US
Overview of Roles: https://help.salesforce.com/apex/HTViewHelpDoc?id=admin_roles.htm&language=en_US
Sharing Rules Overview: https://help.salesforce.com/apex/HTViewHelpDoc?id=security_about_sharing_rules.htm&language=en_US