OpenSourceCMS.com lists nine Open Source Wiki implementations. Three of them are based on ASP and six on PHP. That is by no means a comprehensive list, but OpenSourceCMS hosts live, working demos of each Wiki listed. A more comprehensive list (but without the live demos) is available from Wikipedia (which runs on MediaWiki).
Another technique for identifying which Wiki is best for you, is to think about the goal of your Wiki and look for existing Wikis which have a similar goal. A good way to find existing Wikis is to perform a Google search with the term wiki.
Between the two techniques listed above, you should now have a very short list of candidates. Now is the time to download and install a beta test of each one on your own server. Load it up with data similar to what you that which you will put in your production Wiki. If you can, get some actual users to help with this process and get their input on which Wiki they like best.
After all that, you should have it narrowed down enough to pick your final candidate for a production Wiki. Get it installed and running on your production server, then work on getting that Critical Mass needed to make it a success.
Next time: Building your Wiki community.