Parcel is the best delivery tracker that I've used. Its secret weapon is its Amazon integration: purchases made on Amazon are automatically added to the app. This is exactly what I need, as most of what I buy online comes from Amazon. This feature alone is worth the price of the subscription: just $2.99 per year.
The app itself is bare-bones, which suits me just fine. It's a package tracker and I don't intend to spend much time in it. So long as it displays the information I need – the name of the package, how far away it is, and when it will be delivered – I'm all set.
It supports more than 300 carriers, but the only ones I really care about are FedEx, UPS, DHL, and USPS – and they're all covered. A full list is available on the website.
Push notifications are nice to have, though I usually turn them off. I turn off push notifications on almost every app, in fact. I'll check in when I need to. The only one I leave on is when a package is delivered. That's all I need to know.
The app has a nice map view if you want to see how well-traveled your package is.
Opening onto the main screen of the app without any delivery presents you with bare-bones screen. The top left button lets you change settings, while the "+" button lets you add deliveries. The necessary info is the package tracking number. Because each package delivery service has a standardized method of numbering their deliveries, Parcel automatically infers which carrier is doing the delivery.. If you want, you can add a description. If you have a barcode, you can scan that and skip the manual entry.
You can forward emails to parcel through the web app . Say you order something from Apple. You can set up the Apple delivery email to forward to Parcel so that whenever a new item is shipped, it's automatically added to the app. This helps cut down on the manual work you need to do.