I plan on reading through some Aristotle, and I was wondering if there are any books by him that people consider a waste of time to read. I would like to read through everything eventually, but I know the Greek philosophers in particular can have highly tangential writing styles.
Shane's answer is great overall on what to read, but reading your title and question body again... you asked what to skip.
Skip his Biology in its entirety. There's quite a few texts in there. Mostly interesting only on an anecdotal level (nearly all the primary texts here http://plato.stanford.edu/entries/aristotle-biology/). I'm not saying that it's completely worthless -- just that it will only matter if you want to study a particular subfield in history of philosophy of science.
All of some sections of the Politics can be skipped. Particularly, the lengthy discussions of each political system in the Greek world (BK 2 sections 8-12). Some of them are worthwhile so consult a contemporary commentary that should give you the highlights instead of trudging through the descriptions. Also if you will read both Nicomachean Ethics and Politics, you can skip the second half of NE Book 8.
There are a number of good books about Aristotle that will greatly, greatly aide you in your quest to read Aristotle.
The best single volume introduction to Aristotle's thought currently available in English is Christopher Shields' book Aristotle published by Routledge. Even better, the book is arranged thematically, which will allow you to read one of the primary works, then turn automatically to the relevant chapter for Shields to tell you what has just happened.
Start with the logical works. Read the De interpretatione and the first books of the Prior and Posterior Analytics for Aristotle's ideas on logic and method as well as some important criticisms of Plato's theory of the forms.
Then move to the philosophy of nature works, namely the Physics and De anima. I'd just read the first two books of the Physics, and just book I of De anima.
Then move to the read hardcore metaphysical issues, namely read books I, III, IV, VII and VIII of the Metaphysics.
Then, for a little breather, read the Nicomachean Ethics, the whole thing.
Finish with the Rhetoric and the Politics.
If you read through all that material, together with Shields' book, you'll basically have a good beginner's grasp of Aristotelian philosophy and be ready to start looking in more detail at specific subjects.
St. Thomas Aquinas, considered one of the greatest commentators on Aristotle, only commentated on these works by him:
De coelo et mundo
De generatione et corruptione
De sensu et sensato
De memoria et reminiscentia
And some of his commentaries are only partial (e.g., he didn't commentate on Books 13—Μ & 14—Ν of Aristotle's Metaphysics).
He describes in his Sententia Ethic., lib. 6 l. 7 n. 17 [1211.] which subjects and in what order boys must learn:
[T]he proper order of learning is that boys first be instructed in things pertaining to logic because logic teaches the method of the whole of philosophy. Next, they should be instructed in mathematics, which does not need experience and does not exceed the imagination. Third, in natural sciences, which, even though not exceeding sense and imagination, nevertheless require experience. Fourth, in the moral sciences, which require experience and a soul free from passions … Fifth, in the sapiential and divine sciences, which exceed imagination and require a sharp mind.
This is roughly the order the works are placed in the list above.