Description  Markup  Example 

newline  \\ 

exponent  ^ 
\( x^2 \) 
union  \cup 
\( \cup \) 
intersection  \cap 
\( \cap \) 
space  ~ 

tilde  '\sim'  \( \sim \) 
tilde  ~ outside of TeX 
~ 
backslash  \backslash 
\ 
x over y (division)  x \over y 
\(x \over y \) 
My list focuses on things that work in mathematical formulae without using a package, because that's where I use TeX  for math expressions.
For the copy/paste problem, you can work around it by saving the image to disk, opening with Paint, and copying from Paint.
Equation that is tough to render well:
X(u) = \sum_{n=0}^{N1} x(n)e^{i2\pi un/N}
\( X(u) = \sum_{n=0}^{N1} x(n)e^{i2\pi un/N} \)