Delivery Status Touch (US$2.99) is my personal choice. It supports more than 25 delivery services, like FedEx, UPS, DHL, and the good old USPS. Additionally, there's built-in tracking for packages coming from Amazon, Adobe and, of course, Apple.
You can track several packages at once, and the main screen lists each at launch, sorted by color-coded listings. Shipments are accompanied by a big countdown to the delivery date. Once your goodie gets close, you can bring up a map and watch it approach. Finally, push notifications will satisfy even the least patient among us.
USPS Mobile (Free) lets you track a package sent through the USA's postal system. To get started, replace a shipment's tracking number with a nickname (might we suggest "precious?") and watch as the progress bar slides along, representing its progress.
USPS Mobile also lets you find a nearby post office or collection box, look up ZIP codes, and more. However, for the purposes of this post, we're only interested in package tracking.
UPS Mobile (Free) is for those who prefer to let Brown deliver their iPads. This full-featured app lets you replace a tracking number with a nickname and watch a progress bar move with your package's progress, much like the USPS app does. In addition, you can find UPS locations, create shipping labels, and save your shipping preferences. There's no push notification with this one, so the overly-eager will just have to sit tight.
Track My Shipments+ (Free) does feature push notifications, unlike UPS Mobile. In fact, whenever your package's status changes, you'll get a message. An in-app map shows not only where your package is, but also the direction that it's traveling in.
The neat thing about Track My Shipments+ is that it is part of an online service that tracks shipments for you. Just forward a confirmation email from any of six major carriers to a special email address, login with the app, and your shipment is in place. There's no need to type a lengthy shipping number into the iPhone.
Track My Shipments+ also offers in-app purchases, like the aforementioned push notifications, unlimited simultaneous package tracking, and associate email, which allows you to send messages from multiple accounts.
TrackThis Package Tracking ($0.99) is a great-looking app that supports 13 carriers, including UPS, FedEx, USPS, DHL, TNT, Canadian Post UK City Link, and more. TrackThis also features push notifications, but the nice thing is that you can determine what events deserve notification, like "on truck for delivery" or "delivered." That way, you won't be disturbed by every link in the chain.
There are five apps to feed your obsession for the next 2-3 weeks. Enjoy your perseveration!