At TeachThought, we often provide lists of digital resources, and many of them are apps.
Apps for struggling readers.
Apps for struggling writers.
Apps for project-based learning.
Any while many of these apps are for students, the following list of apps from Sam Gliksman can be considered for both teachers and students, and an excellent foundation slew of apps for any 21st century teacher. From GoodReader and Slide Shark to Printopia and Air Display, all fill different niches of 21st century learning, and the many possibilities the iPad affords.
Owner
Educator's Essential iPad Toolkit
Listly by Sam Gliksman
Essential toolkit of core apps you need for personal and educational productivity and everyday reference.
The search service that has become a verb. Go ahead and Google it.
The ad free version of Dictionary.com Dictionary & Thesaurus for the iPad
Available in both regular and Pro versions, Pocket Informant helps you manage your life. Includes a multi-featured Calendar, Task lists and more and syncs with your Google account.
If you don't have a Twitter account yet then get one. Twitter is a great way to connect and learn from other educators. Use the #iPadEd hashtag to follow educational iPad tweets.
Creates a beautiful magazine by connecting to your custom news feeds and social networking contacts.
PhotoSync wirelessly transfers your photos and videos between devices and computers. It's the simplest way to move media content to and from your iOS devices. Great for collecting media from students on a teacher laptop.
Splashtop connects your iPad to your laptop or desktop. Access and use any programs or files even when you're not at your computer.
Extends your computer desktop so that your iPad acts as a second screen. Just move content from one screen to the other as if they were connected.
Printopia
This one isn't an app - you install it on your computer. Run Printopia on your Mac to share physical and virtual printers to your iPhone, iPad or iPod Touch. Incredibly versatile.
Connects to your cloud storage accounts. Downloads and reads all sorts of different file types. It's the swiss army knife of document processors for the iPad.
Dropbox
Most popular cloud service and connects to many apps on your iPad making it easy to pull down and push up content.
Pocket (Formerly Read It Later) enables you to store anything you want to read, take it with you offline and read it whenever you have time. You can also share what you're reading with your colleagues.
TED
Smart people, smart ideas... all on video. Great for stimulating thinking out of the box.
Evernote
Clip, store or create all types of digital content in Evernote notebooks. Sign up for an account at evernote.com. There's 101 ways to use Evernote effectively both personally and in class.
Kindle
Just a wider range of choices than iBooks and very useful when you need that particular book.
Pages
If you're into serious word processing then this is the app you'll want to use. With a variety of templates, styles, charts and more, Pages is the closest you'll get to full featured word processing on an iPad.
WolframAlpha
Go ahead... ask it whatever you want. My bet is that it knows the answer.
Notability
Notability powerfully integrates handwriting, PDF annotation, typing, recording, and organizing so you can take notes your way! Discover the freedom to capture ideas, share insights, and present information in one perfect place on iPad.