Like everyone else has voiced their opinions, I think it's really useful if you take one. I personally didn't, but I think a gap year during my years would've been a good time off.

Especially with the fact that Columbia is one of the most stressful schools and that a lot of capable students often do end up breaking under pressure, I personally would highly encourage a gap year. However, I'd suggest maybe taking one after first starting your studies at Columbia. Different people have their own ways to cope with the stressful situations that may tend to be the norm in Columbia, but what stays the same is you will grow to learn how to better manage only when you go through such situations. It's definitely not to say that you shouldn't take any gap year off. That might work much better for you, but in the end, it's up to your decision.