I believe if you have access to a report, record level access can be ignored and you can potentially see all records. Does this apply at the object level of a profile? So say a report is on Accounts, and your profile has No Access on the account object. Technically, you shouldn't be allowed to view that report, right?
Reports honor object, record, and field level security. You cannot run a report for a data type that you don't have access to. This is true even if you have access to the report (e.g. it is in a Report Folder or Dashboard Folder you have access to). Please note that Dashboards allow users to see the generated charts even without access to the underlying data, but will not be able to see the report details.