The simple solution
As long as the super- and subscripts of the summation signs are narrower than the sign itself, the solution is quite simple:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
\text{maximize } &\sum_{j=1}^{n}p_j x_j \\
\text{subject to } &\sum_{j=1}^{n}w_j x_j \leq c, \\
&x_j \in \{0,1\}, j = 1, \ldots, n.
\end{align}
\end{document}

The more sophisticated solution
As soon as one of the super- or subscripts gets wider than the sign, this will break the alignment (note eq. (2)):
\begin{align}
\text{maximize } &\sum_{j=1}^{n}p_j x_j \\
\text{subject to } &\sum_{j=10000}^{n}w_j x_j \leq c, \\
&x_j \in \{0,1\}, j = 1, \ldots, n.
\end{align}
As everything is aligned at the most left part after the &
sign, the alignment happens in eq. (2) at the "j" subscript, making the sum signs no longer stand right below each other:

But there is help! The mathtools
package provides a command called \mathclap
that in principle sets the box width of its argument to zero (for exact explanation cf. http://math.arizona.edu/~aprl/publications/mathclap/perlis_mathclap_24Jun2003.pdf). If we use this, the alignment will work even if the descriptors of the sum sign are wider than the sign itself, by allowing the descriptors to slide over the alignment barrier:
\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}
\begin{document}
\begin{align}
\text{maximize } &\sum_{j=1}^{n}p_j x_j \\
\text{subject to } &\sum_{\mathclap{j=10000}}^{n}w_j x_j \leq c, \\
&x_j \in \{0,1\}, j = 1, \ldots, n.
\end{align}
\end{document}

align
oralign*
environments from the AMS packages, with&\null
as your separator and\text{}
for text. – Sean Allred Jun 19 '13 at 22:25