Many, if not all, of the trackers and wikis that I have encountered allow anonymous access if you decide to enable it - the reasons that this is rarely done are a) traceablitly, b) feedback & c) the amount of low quality/dubious content that such services rapidly accumulate otherwise.
To enable such access you, as administrator of the tracker or wiki, need to look for settings with elements such as "Require Logon" or "Allow Anonymous Posts" - these are usually specific to the given tracker or blog so that you can have internal only and anybody trackers and define different workflows for them. Both trac and gforge allow you to set a specific tracker as not requiring a login.
One example for wikis is the MediaWiki as used by Wikipedia which does allow anonymous edits but flags them for more careful moderator attention to reduce the huge amount of libel, spam, misinformation and damage that such edits would otherwise cause.
Do keep in mind that if you have anonymous tickets or wiki entries then you will not be able to give feedback, (such as this is fixed), to the originator of a ticket and you will be facing a huge amount of work policing tickets such as "it doesn't work" and wiki entries such as "don't try this bit it is fun" or "isn't so and so hot/nasty/useless", etc. If you require a log in you can at least get back to the originator for more details, a clean up, lock them out or ask for the phone number whichever is appropriate.