So far, all of the following have been suggested as really important, either more important than the others or at least as important. In alphabetical order:

• algebra
• calculus
• logic
• probability and statistics
• programming
• trigonometry

And number theory got an honorable mention for being awesome.

How are people judging what is more important than what? I hope not by looking at how often they use these things themselves.

Not a month goes without my having occasion to use all of these, and 3D geometry, and other mathematical stuff as well. But as an applied mathematician and programmer, I would, and they all seem to me like just a step beyond basic arithmetic. It would be easy, too easy, for me to say that everyone should know this stuff, so I won't.

Instead, FYI and FWIW, here's the current high school curriculum in the UK for A-level maths.