Hi Jeremy,
Your question is a tiny bit open-ended :)
Chances are, you will find modules for whatever analysis you want to do in the UIMA framework:
Unstructured Information Management applications are software systems that analyze large volumes of unstructured information in order to discover knowledge that is relevant to an end user. An example UIM application might ingest plain text and identify entities, such as persons, places, organizations; or relations, such as works-for or located-at.
UIMA is made of many things
UIMA enables applications to be decomposed into components, for example "language identification" => "language specific segmentation" => "sentence boundary detection" => "entity detection (person/place names etc.)". Each component implements interfaces defined by the framework and provides self-describing metadata via XML descriptor files. The framework manages these components and the data flow between them. Components are written in Java or C++; the data that flows between components is designed for efficient mapping between these languages.
You may also find Open Calais a useful API for text analysis; depending on how big your heap of documents is, it may be more or less appropriate.
If you want it quick and dirty -- create an inverted index that stores all locations of words (basically a big map of words to all file ids in which they occur, paragraphs in those files, lines in the paragraphs, etc). Also index tuples so that given a fileid and paragraph you can look up all the neighbors. This will do what you describe, but it takes quite a bit of tweaking to get it to pull up meaningful correlations (some keywords to start you off on your search: information retrieval, TF-IDF, Pearson correlation coefficient).