I want to make a scarf, knitting vertically on circular needles. How long should the cable be if I want the scarf to be 60"?
Let me make sure I understand your question. You're saying that you're going to cast on LOTS of stitches - like the full 60" length's worth, not the few stitches that would be the width of the scarf, right? If that is the case, you could probably get away with a 32" needle, but it's still going to be packed with stitches. I think you would be more comfortable with a 48" length, although I suggest that if you are going to have to purchase a needle to do this, I'd even go with a 60" needle if you can find one in the size you need. That way, you can use it later for magic loop (or whatever).
Yes. I'd be casting on 60 inches of stitches. If I buy needles with such a long cable, will I be able to use them for regular projects or will it be too uncomfortable?
Well, yes they could conceivably get in your way if you are working with only 20 stitches or so, but you will be very unhappy if you buy 32" needles and have to struggle to move 60" of stitches around. This could be a good opportunity for you to try KnitPicks Options or Harmony needles. Buy the size tips you need for this project and a 60" cable, and another smaller cable (actually, they come in pairs). Their shipping is very reasonable and you may find that you love them so much that you will want the set.
Are you using worsted weight yarn? Seems like I used a 36" circular when I did my wallaby sweater (looks like a hoody) and since I am pretty fluffy, the bottom measures about 60". Size 10 needle, I think. The stitches weren't too tightly packed on the 36". You can go 40 and it will be a bit better, but I don't think you need a 60" circular.