As with any product or service, your inherent risk assessment should inform you of the types and amounts of risks in any product or service. Couriers, in particular, can be moving anything from legal documents requiring a signature to marketing materials requiring approval to sensitive intellectual property or, in extreme cases, medical equipment or human organs for transplants. There is not a single one size fits all category for couriers. But based on your business, you should be able to define reasonable tiering based on what they carry for you.
I might recommend having some documented standards about what can/can't be sent by courier and reserving a single company or two for the most sensitive data or materials. Those companies should have the highest security standards and courier tracking methods, including GPS location and time stamps, and tamper-proof carrier pouches.
From a due diligence perspective, all courier companies should background check and bond their employees; appropriate insurance is also necessary. They should also be able to provide their chain of custody, information security, and privacy policies.
I hope this information is helpful, but I would also love to hear from other members.