MantisBT is a php/{my,postgres}sql based bug tracker - it's newer to the game than bugzilla & seems to have a solid feature set. Notable projects using Mantis: VTK.
There seems to be a lot of praise about ease of setup and use of mantis compared to other systems.
To kick the tires I checked out vtk's bug tracker, the mantis demo install & I also installed it on my personal webserver. It was very easy to install and get up and running. I haven't tried upgrading but the install was so easy I would imagine the upgrade path would be solid as well.
Search works well. Advanced search filter page is useful (maybe overwhelming at first?) You can create custom search filters and share them across users & projects. You can subscribe to RSS feeds of searches (great feature!)
Support for custom fields looks pretty extensive: you can validate things using a regex, require fields on different actions (submit, update, etc). Support for notes from other users & file attachments. Supports assignment of relationships between issues ( duplicate, parent, child etc)
Support for different access levels (viewer, reporter, developer, admin) This type of control is necessary to allow users to submit bugs, but ensure only developers can assign them etc.
Issues grouped by target release are assigned to 'Roadmaps'. These concisely show all the issues for a release and which are still pending - I think this would be a very useful tool for release management. To use these the project admin has to create "unreleased" versions & the user must set the "Target Release" under the advanced issue options - seems a bit obtuse at first but I don't think its a deal breaker.
Supports multiple project and subproject trackers. This support could be useful for collaboration on large feature sets. For example, many of our 2.0 projects use tables on wiki pages to track things - I think sub projects would fill this role better.
One thing I found a bit annoying is the confirmation message after pretty much any operation: --- Operation successful. [ Click here to proceed] --- You don't have to click - It will eventually take you to the page proper page, but it just feels a bit discontinuous.
Seems powerful & flexible enough to do the job - easy install and administration are definite plus if we end up having to take care of hosting. My only nits are really minor UI issues - these could be resolved with a more web 2.0 like interface.