Deliveries 6.0 for iOS
Deliveries for iOS — formerly known as Delivery Status Touch before its version 6.0 update — is the best app for tracking shipments. How do we know? Over at our sister site The Sweet Setup, we tested several package trackers and found that Deliveries has everything we want in such an app.
It provides a number of ways to easily add tracking codes, it color-codes shipments based on the carriers delivering them, it ties into Notification Center so you always know what's happening with your orders, and it syncs nicely between your iOS devices and the Mac app. There's really no better way to track your stuff from order to delivery.
The universal iOS app and the Mac app are each $5.