<p>When developing a database of articles in a Knowledge Base (for example) - what are the best ways to sort and display the most relevant answers to a users' question?</p>

<p>Would you use additional data such as keyword weighting based on whether previous users found the article of help, or do you find a simple keyword matching algorithm to be sufficient?</p>

That's a hard question, and companies like Google are pushing a lot of efforts to address this question. Have a look at
Google Enterprise Search Appliance
or
Exalead Enterprise Search
.
Then, as a personal opinion, I don't think that any "naive" approach is going to improve much the result compared to naive keyword search and ordering by the number of views on the documents.
If you have the possibility to expose your knowledge base to the web, then, just do it, and let your favorite search engine handles the search for you.