Yes, you want a stemmer. Lauri Karttunen did some work with finite state machines that was amazing, but sadly I don't think there's an available implementation to use. As mentioned, Lucene has stemmers for a variety of languages and the OpenNLP and Gate projects might help you as well. Also, how were you planning to "chop them up"? This is a little trickier than most people think because of punctuation, possesives, and the like. And just splitting on white space doesn't work at all in many languages. Take a look at OpenNLP for that too.
Another thing to consider is that just comparing the non stop-words of the two documents might not be the best approach for good similarity depending on what you are actually trying to do because you lose locality information. For example, a common approach to plagiarism detection is to break the documents into chunks of n tokens and compare those. There are algorithms such that you can compare many documents at the same time in this way much more efficiently than doing a pairwise comparison between each document.