One of the new toys I got for Christmas this year was a TI-89 Titanium. We don't allow the use of this particular model at McNeil High School for Algebra II (we DO allow 83's and 84's... but not 89's). Ironically, I bought this on eBay from a student in North Dakota who wasn't allowed to use it in his math class (but didn't realize it until after he bought it).
Here are a few examples -- in the form of recent test questions and how the 89 takes all of the thinking (i.e., the fun) out of the problems -- of why we don't allow them in Algebra II.
Just type in the binomial expansion, hit enter, and... voilà!
Here's one of the factoring-sum-of-perfect-cubes problems that everyone loved...
This one's great... it'll find all the roots, and even keep the irrational ones in exact radical notation:
...and this is barely scratching the surface of what the 89's are capable of. If you happen to have a TI-89, I personally think they're a great tool to use to check your answers... but don't use them to do your Algebra homework for you (or else you're cheating yourself). Then again, you can find tools to do all of this stuff online as well.