Sherri just posted about something called PHP Surveyor, which looks nice and nifty, but I don't know anything about PHP and SQL, and I'll be most of you don't either. Just the other day, a colleague pointed me towards a free hosted assessment tool called FAST, which stands for (are you ready?) Free Assessment Summary Tool. It was built just down the road at Mount Royal College here in Calgary, and pretty much offers what the name suggests.
FAST allows you to build any number of brief assessments that you can point your students to. You can view your results in all sorts of ways, and can download to Excel. You're limited to 20 questions, but the creators say that's to encourage higher completion rates. Types of questions you can create: yes/no, Likert scale, multiple choice, long answer, yes/no & long answer, Likert scale & long answer. There's a PDF brochure that shows nice screenshots and answers some FAQs about the product.
The biggest potential downside that some of you might find is that because it's hosted at Mount Royal College, that institution's logo appears at the top of the page instead of yours, but if you want to host it at your place that can be done for a price.
There's also a nice database of suggested generic questions if you're having trouble getting started...
This is definately something I plan to start using in the New Year (my first resolution!) to help gauge the effectiveness of my online instruction.