If you just create new sandbox or refresh a sandbox Sandbox, you will not able to send email: manually, from workflow or from apex code. This is because since Spring '13 release, Salesforce has change email deliverability to System email only.
You can change the email deliverability to All email from Setup > Email Administration > Deliverability.
If system administrator have not change email deliverability, user will not see Send an Email button in Contact, Lead or Case related list, although it is has added to the object related list page layout.
From Workflow or Auto-Response Rules, email will not send out and there is no notification.
From apex code, you will found this error "Email Privileges Revoked", see this blog.
You can check Email Logs to audit all email send from and to Salesforce, email logs accessible from Setup > Logs > Email Log Files.