You're using math mode incorrectly, and therefore TeX has no idea where a good line break should be placed despite using \raggedright. Below I've formatted the equations in the proper way, allowing for a line break to be placed around a relation (like =). I've also added some formatting style that should make your code more readable.

\documentclass{article}
\usepackage{algorithm,algorithmic}
\newcommand{\var}{\textit}
\newcommand{\proc}{\textbf}
\newcommand{\prop}{\texttt}
\newcommand{\plusplus}{{+}{+}}% Other options: https://tex.stackexchange.com/q/4302/5764
\begin{document}
\begin{algorithm}
\caption{Iterative Process}
\begin{algorithmic}[1]
\raggedright
\STATE \proc{OwnerClassPrediction}()
\STATE $\var{iteration} = 1$
\STATE $\proc{Predictions}(\var{iteration} - 1) = \prop{methodTraceList.predictions}$
\STATE $\proc{Predictions}(\var{iteration}) = \emptyset$
\WHILE{$\proc{Predictions}(\var{iteration}) \neq \proc{Predictions}(\var{iteration} - 1)$}
\STATE $\proc{Predictions}(\var{iteration}) = \proc{SurroundednessPurePattern}(\proc{Predictions}(\var{iteration}))$
\STATE $\proc{Predictions}(\var{iteration}) = \proc{SurroundednessMixedPattern}(\proc{Predictions}(\var{iteration}))$
\STATE $\proc{Predictions}(\var{iteration}) = \proc{InheritanceInterfacesPattern}(\proc{Predictions}(\var{iteration}))$
\STATE $\proc{Predictions}(\var{iteration}) = \proc{AllCallersPattern}(\proc{Predictions}(\var{iteration}))$
\STATE $\proc{Predictions}(\var{iteration}) = \proc{AllCalleesPattern}(\proc{Predictions}(\var{iteration}))$
\STATE $\var{iteration}\plusplus$
\ENDWHILE
\end{algorithmic}
\end{algorithm}
\end{document}
I don't really enjoy the indentation associated with the automatic line breaks from \raggedright. You could consider manually breaking the content and inserting some indentation (\quad) manually.

\documentclass{article}
\usepackage{algorithm,algorithmic}
\newcommand{\var}{\textit}
\newcommand{\proc}{\textbf}
\newcommand{\prop}{\texttt}
\newcommand{\plusplus}{{+}{+}}% Other options: https://tex.stackexchange.com/q/4302/5764
\begin{document}
\begin{algorithm}
\caption{Iterative Process}
\begin{algorithmic}[1]
\STATE \proc{OwnerClassPrediction}()
\STATE $\var{iteration} = 1$
\STATE $\proc{Predictions}(\var{iteration} - 1) = \prop{methodTraceList.predictions}$
\STATE $\proc{Predictions}(\var{iteration}) = \emptyset$
\WHILE{$\proc{Predictions}(\var{iteration}) \neq \proc{Predictions}(\var{iteration} - 1)$}
\STATE $\proc{Predictions}(\var{iteration}) = {}$ \\
\quad $\proc{SurroundednessPurePattern}(\proc{Predictions}(\var{iteration}))$
\STATE $\proc{Predictions}(\var{iteration}) = {}$ \\
\quad $\proc{SurroundednessMixedPattern}(\proc{Predictions}(\var{iteration}))$
\STATE $\proc{Predictions}(\var{iteration}) = {}$ \\
\quad $\proc{InheritanceInterfacesPattern}(\proc{Predictions}(\var{iteration}))$
\STATE $\proc{Predictions}(\var{iteration}) = {}$ \\
\quad $\proc{AllCallersPattern}(\proc{Predictions}(\var{iteration}))$
\STATE $\proc{Predictions}(\var{iteration}) = {}$ \\
\quad $\proc{AllCalleesPattern}(\proc{Predictions}(\var{iteration}))$
\STATE $\var{iteration}\plusplus$
\ENDWHILE
\end{algorithmic}
\end{algorithm}
\end{document}