Speaking from a EE perspective
As per Kim, definitely go for as general a course as you can. So not as per Kim, don't go for 'Avionics' or whatever, go for vanilla CS, or even a joint CS-Maths degree if that takes your (or rather, his) fancy. There will be stuff that you think you're interested in beforehand but which turns out to be either hard or boring, and there will be other stuff that you didn't think you'd like until you get there. Similarly, try to go for a department that is part of a larger faculty so you can move around a bit if you want.
A case in point: muggins. My degree is in Electronic Engineering, which is notable for the absence of a "Electrical and ... " prefix; unlike most EE (a.k.a. EEE) departments, mine had no power engineering courses. I ended up specialising in electromagnetic stuff that was right up next to that sorta thing, and a couple of those courses at undergrad could have opened up a whole new sector of jobs to me. Not to worry, I've done okay for myself but I do see a whole load of people in industry who have physics degrees and are also doing perfectly well for themselves. It's always easier to specialise later rather than try to climb out of the over-specific hole you've dug for yourself.