Very possible, but depends
This question of using an iPad as your primary or only computer has been coming up a lot lately because the device is becoming more and more capable.
It really depends on your needs, but I think most people could simplify their lives by using an iPad as their personal computer. I would preface this by saying that I assume most people's work requirements are covered by a computer provided by their employer. They have no say in the device, and do not use it for personal content....it's off limits for security reasons.
For me, essentially all of my personal computing needs are met by the iPad. Well, I have an iPhone and Apple TV too. In a few places, I have made some compromises to gain simplicity and convienance. For example, I used to store all photos on the family Mac. Now, I use Flickr, and I am more selective about uploading. Of course, it forces me to weed through the duplicate and crummy pictures, but the cloud makes the photos available for sharing with the grandparents. We use Dropbox for documents, so the kids can work on homework anywhere. For movies and music, I stick to only iTunes and streaming content...and I am still overwhelmed by the vast amount of media available to me.
I know the idea of making a few compromises in ones personal digital life will seem crazy to some folks on this Forum. The trade-off is worth it to me. Anyway, this is how I use the iPad:
Email
Calendar & Reminders
Contacts
Web browsing - Safari
Web Apps - CNN, Weather, Web MD, Wikipedia, UTube, Podcasts, Facebook, Twitter, etc.
Finances - Mint and Banking Apps
File Management - Drop box, Goodreader
Books & Education - iBooks, iTunes U, Kahn mobile
Media organization & editing - iPhoto, iMovie, GarageBand (iLife)
Media storage (photos and video) - Flickrstackr, photo sync, photo stream
Music - iTunes, Pandora (streaming)
Movie streaming - Netflix, HBO2Go
Productivity - Notes, Pages, Numbers, Keynote (iWork)
Utilities - find my phone, find my friends, *Remote, Airport, FaceTime*
Device settings and In-App backup & storage - iCloud