why not. Redmine (for example) comes with 3 trackers out of the box and allows you to create more. The 3 are bug, feature and support.
bug is obvious, but is feature request a developer thing, or more a design/management issue? What of support - it might not be a bug but a configuration issue.
You can easily add Requirement to the list.
The benefit of adding all these to the same tracker tool is that you can then link them together. Imagine someone creates a feature request that goes through several modificatons through discussion with architects or designers. When management decides to implement this, it can be associated with a 'work' tracker item for you to check your source against, and then associate it with a 'test' tracker as it goes through QA, and then can be associated with support or bug items in the future.
This is called 'traceability' and is huge thing with large scale or very controlled software projects. As long as you don't add onerous workflows to it (ie only a team lead can create a work item, etc) then its a very good thing.