Hmm...
I survived high school without a laptop (well I got one in year 12 - but never brought it to school). The thing that annoys me is that you don't learn cursive handwriting (my mum is a pro and it looks much neater than my handwriting). With any handwritten assignments I have to have my handwriting perfect (if not I'll throw it out and start again).
At uni you will definately need one. Anyone doing engineering, physics, chemistry, the applied maths (pure maths doesn't need computers - I think). But with lectures, don't type your notes (time to turn on computer and load it = time missed out on learning). Instead bring a hard copy of the lecture notes and scribble over them (this allows you to highlight key parts of your lecture).
End of the day, you only need a computer for assignments and emails. As you go further, you do more assignments.