Algebra is a MUST for anybody going into CS. You need to have rock-solid algebra, and should probably be very comfortable with basic mathematics. Enjoying math certainly doesn't hurt when you're reading code all day. The idea of order of operations needs to be understood on a completely fundamental level.
Propositional logic IS Computer Science. Strong logic is a MUST.
As some people have said, thats really all you "have" to know for CS. You could learn basic programming from there, and go on to design website code and work on UI and all sorts of things like that. However, you're going to be very limited.
After that, different areas require different skills. Very quickly you're going to need a very solid understanding of pretty heady math.
Any sort of graphics programming is going to require you to be AMAZING at trigonometry, geometry, vectors, matrices and working in 3D space. Calculus would likely be useful.
CS Research or Scientific Computing / Programming is going to require a very solid understanding of Statistic, Calculus, Physics, and DiffEq.
Anything beyond Calc 2 or DiffEq is unlikely to be useful in CS.
Here's the thing, the way I see it. You don't need Calc 2 to be able to learn enough CS to program a Hello World. With a solid graphics API, you could even get away with coding asteroids or a chat program. But your understanding of what that API is doing is going to be limited. More importantly, though, is that CS != programming. There's more to CS. On the one hand, you could get by without being good at math if you were really good at the other parts of CS: lateral thinking, software design and objects and things like that.
However: If you're not good at math, its likely because you don't like math. If you like math, then just go study it some more, learn it, and you'll enjoy it, so you'll just get better and better. It seems to me most of the people who aren't good at math must be a subset of those who don't like math. And while not knowing advanced math may not be a problem, if you don't like math, odds are you aren't going to enjoy computer science. They're very similar. Complex abstract logic, formulas, functions, numbers, etc. Its indicative that you probably shouldn't be doing this. I think a good understanding of math would be helpful to programming in an abstract way too; seeing an axiomatic system of mathematics taken to such a high level of proofs helps you visualize complicated systems later on.
If you want to be a programmer, you don't need math, but it helps situationally.
If you want to be a Computer Scientist, you absolutely need math.
Colleges teach to academics, so they should absolutely require math. Colleges also require a general education; I assure you my Texas History courses never helped in my CS work at all. If anything, math is a million times more relevant than other core classes.
That said, I'm sure you can learn programming at night school or community college without being forced to take math. Its just if you want a Computer Science Degree. And a computer science degree implies that you know how to handle complex functions.