Yes, HIPAA compliance strictly requires properly disposing of patient health information.

Google Apps even has specific services for companies needing HIPAA compliance: https://support.google.com/a/answer/3407054?hl=en

If the material includes sensitive personal information, privacy laws may require that the information be destroyed or "put beyond use" within a certain timeframe after the information is no longer necessary.

You might also, for example, have contractual obligations with another company to delete business confidential information after the end of the contract.

Many corps operate 'compliance smoothing' in which materials are proactively deleted. Where I worked all e-mails were purged after 90 days unless the user manually saved them elsewhere.

If your legal tells you the legal from another entity wants their correspondence deleted, for some valid reason, you are compelled to carry that out.