How many publications are available for these devices? Amazon lists 756,053 ebook titles, while B&N states that they have over 2 million books and magazines. Apple lists "tens of thousands of books" in available via iBooks, but that's not quite the whole story. There are Nook and Kindle apps for the iPad, so the B&N and Amazon libraries are both accessible, giving the iPad the largest total library of content. When trying to choose a device, search for books your are planning to read in the different bookstores and see who has what you want.
Size and weight
The Kindle and Nook are both roughly the height and width of a paperback book, and .5" thick. The 3rd generation Kindle is slightly smaller and weighs less than 9 ounces, the Nook comes in at about 12 ounces. The iPad is considerably larger at 9.5" x 7.5" x .5" and 1.5 pounds. I find both the Nook and Kindle comfortable to hold and read for hours at a time, while the iPad can get be a bit uncomfortable on long reads.
The iPad uses a 9.7" LCD display, like a computer monitor. Both the Nook and Kindle use a 6" e-ink display. E-ink is a fairly new display technology that seeks to emulate a printed page. Black and while only (for now) and not back-lit, you'll need an external light source for reading - just like a real book. The main advantages of e-ink are battery life, readability in sunlight or outdoors, and low eye fatigue. Eye fatigue is very subjective; some people are very susceptible and it doesn't seem to bother others at all, but is something to take into consideration. The choice here really comes down to two issues - where will you use it, and what types of content will you read? The Kindle and Nook are black and white, so comic books and color magazines are out. If you want to read outside, the iPad is all but unusable. As a side note, the Nook does have a small color touchscreen at the bottom of the unit which displays a virtual keyboard, book covers, etc. I say it's a side note because it's not really used when actively reading.
As noted in a previous post, the iPad gets about 10 hours of use. This is excellent for an LCD display device. On the other hand, e-ink displays only use power when you change the display - in this case, flip to the next page. It requires no power to keep the image on the screen. Because of this, you may not have to charge a Kindle or Nook for a month. Really, a month. You can easily travel with these readers and leave the charging cord at home.
Here is another big split. For the Kindle, the wifi only and wifi+3g models cost $139 and $189 respectively. The Nook models are $149 and $199. The iPad starts at $499 for the wifi only version and $629 for the 3g in the 16GB models.
Kindle - 4GB
Nook - 2GB, expandable via microSD slot to 16GB
iPad - 16GB-64GB depending on model
This really is not an issue with e-readers. Considering 2GB is enough storage to hold 1500 books, most users will not run into a storage capacity limitation.
No definite winner here; it really depends on what is important to you. If you just read novels, want to read outside and don't want to have to charge every day - the Nook or Kindle is the way to go. If you want to read comic books or magazines or anything with a lot of pictures or color diagrams and have no desire to read it on the beach, the iPad does a great job and gives you the best of both worlds as far as access to content in all of the ebook stores.