How can including an IV uncorrelated with the DV improve a multiple regression model? Let's say $Y$ is my DV, and $X_1$,and $X_2$ are IVs:
\begin{align}
\newcommand{\Cor}{\rm Cor}
\Cor(Y,X_1)   &= 0.7994172  \\
\Cor(Y,X_2)   &= -0.00041   \\
\Cor(X_1,X_2) &= 0.505      \\[10pt]
R^2_{Y|X_1X_2} &= 0.9315   \\
R^2_{Y|X_1}    &= 0.624    \\
R^2_{Y|X_2}    &= 0.00038
\end{align}
Can any one explain this? I don't understand how this could happen.
 A: tl; dr: A low correlation does not mean that your variable is useless in the final model.
To answer your first question (can a multiple regression contain a IV that is not correlated with DV) 
Yes, a multiple regression can contain an IV that is not correlated with the DV.
Assuming that you're only asking about linear regressions: 
A multiple regression equation can and often will include independent variables that are not correlated at all with your dependent variable. In a simple regression (i.e. $Y$ ~ $X$) correlation is directly related to the R-squared, and so a low correlation pretty much means that a linear model will have a low R-squared. 
However, in multiple regression, there are a few situations where variables will have low correlations but still be useful in the model. 
For your second question:
There's some sort of interaction between $X$1 and $X$2 which helps in understanding your Y. If you were to look at the regression coefficients in your linear model, there's a good chance that you'd find that both are statistically significant. 
