Another vote for FogBugz. Works great, can easily do everything the original poster mentioned. Plus it is extensible if you really need to build you own hooks into it. You can try it out online completely free for 45 days (and they'll even sometimes extend that if you ask real nicely) and then if you decide to use it, you can either pay to use their hosted service or if you purchase it for local use, then they'll even send you the database for you to re-install locally so you loose no time migrating your trial period data. It makes it easy for you to publish the information to others on a need to know basis and if you are having any trouble getting input from other persons or groups within the company as to how things need to be prioritized, it makes it a great centralized way to put it in front of the faces of the decision makers. The user interface is a little deceiving, as it looks a little overly simplistic at first glance, but it has an excellent and well organized interface for a browser based application. Just spend a little time with the free demo and really put it through the paces and this will become more apparent as you use it. For the value it provides, I consider it to be reasonably priced. If you already have the hardware resources in-house to run it locally, it is much more cost effective to buy it and run locally of course. But if you have any difficulty getting buy-in on it, the monthly service beyond the free trial period makes it very easy for anyone to digest to make sure you have more than adequate time to really have it prove its worth in your organization. I've had to force some customers to sit down and use it to manage their own projects, but once they get over their issues, they find it an invaluable tool without fail.

The free microsoft search server express does exactly that. Plus it is very extensable if you want to write some code for it. Free download at:
http://www.microsoft.com/enterprisesearch