The Slice app sends you updates at every stage of the shipping process. You'll know when a package is out for delivery and when it lands at it's final destination. Not only that, but Slice will also give you a heads up if a price drops right after you bought it. It works with the Apple Watch, too. Slice is free for iOS and Android.
ParcelTrack integrates shipments from more than 50 delivery services into a single app. this keeps you on top of delivery status. ParcelTrack predicts just when packages will be delivered. It also has a feature that keeps a record of everything purchased, making it easy to quickly reference. The app is free for iOS and Android.
Aftership also organizes all your tracking numbers in a single location. It provides notifications of each package you're expecting at every stop along the way. The thing that makes Aftership unique is the number of carriers it works with, a whopping 430 and growing. The app is free for iOS and Android.