I am an undergraduate and used my iPad for study quite extensively in the past year. I have mixed feelings about it, but on the whole it is not at all a bad idea.
So what books could you store on an iPad? I didn't use my iPad for all my courses, but just a few. If a course has digital course notes, slides and other material it is an excellent way of storing these on an iPad. Unfortunately, videos might not always work properly and anything requiring Flash Player will fail. What I found extremely useful was doing old exams using my iPad (saves printing work if you don't have a printer and works more convenient than a PC).
Then about the apps that will allow you to read. The iPad has the programme iBooks built in, and using this to read books in general works quite well in my opinion. Unfortunately, it does lack a function to easily browse to a page you are looking for. The scroll bar on the bottom doesn't really work well anymore with thick books, as you can only approximate the location of the page you are looking for. Turning pages one by one takes considerably more time than with a real book because its design tries to prevent accidental turning by touching the screen (you have to wipe a lot for just a few pages ;)). Another downside compared with real books in my opinion is that you are unable to make notes and underline important information. Fortunately, there is also Adobe Reader for iPad, which works much smoother in turning pages and finding relevant information. Browsing through digital versions does make it easier to find specific information you are looking for using the search option. Also, in Adobe Reader you can underline and highlight important text (if the pdf file allows; scanned files might not work). If you are used to underline quite a lot in your textbook as I am, then the experience might feel a bit less natural and more time consuming on an iPad, but it at least it works.
I will keep GoodReader in mind as well and try that out some time.
Storing all books in your iPad is a good way to ensure you won't forget to bring a certain book to class. On the other hand, you have to watch your batteries carefully ;).
The reading experience is not as natural as a book or even an e-Reader. Reading from an iPad feels quite the same as reading from a screen, so it depends on whether you are comfortable with that. Compared with some modern e-Readers, my eyes tire quite quickly during reading sessions on the iPad.
Next semester I am going for more paper books, but I will continue to use my iPad for digital files including lecture notes and slides. I would say it is good substitute for a laptop computer in class, although you might want to get a compatible keyboard if you want to type text. It is just short of truly replacing one (apps are more limited than PC programs), but using it for mail, reading digital material, surfing in general (forget Flash sites) and storing files works fine.