I personally don't think I could get through university without a laptop. I'm the type of person who downloads the lecture slides (if the lecturer has made them available prior) and then types up some of what the lecturer says in the same document, so I end up with a thorough batch of notes. Without having a laptop, it wouldn't be possible for me to do this, unless I watched the lecture online (which I never end up doing).
You also might want to consider if you had to do group work in a tutorial; not having a laptop can be difficult in that case, especially if you need to submit an assignment that same day, which does happen in some units!
Ultimately, it depends on how you personally learn. My brother went all out by building a custom-PC and buying a Mac, but unless you're rolling in money, it's a pretty extreme solution.