USPS policy is to deliver packages to mailboxes whenever possible, providing they are small enough to fit in the box. If not, and there is no signature confirmation purchased, the package will typically be left as close to the mailbox as possible, such as on a front stoop or porch.
UPS has a policy similar to USPS's regarding packages with no signature requirement purchased. However, if one is purchased by the sender, UPS will attempt to deliver the package in person to the recipient three times before returning it to the sender. If no one is home, UPS leaves a note stating they were there for delivery.
If you have concerns over whether a package can be delivered to a mailbox, using either USPS or UPS, it may be best to send it with some type of signature requirement. That way, you can be assured that only the recipient or his authorized representative will have access to the package.