Hi! We are using Rational RequisitePro for Requirements capture and Rational ClearQuest for subsequent tracking. It works great, but it takes some time to develop a good policy for using RequisitePro and to code the process into ClearQuest. There are also other tools similar to RequisitePro, but they are as expensive as it is.
It depends on the size of the project you are working on. If it is not more than 200 requirements, just use spreadsheet to capture them and track their status. Sortingby columns, which you find in Excel (e.g.) helps. To track bugs (and even tasks), use Bugzilla -- it's a free Perl script.
Also you should know that RM is a large thing. There is a lot about it besides tools.
First, a good Requirements Analysis policy is highly recommended. You should at least create templates for the FIRST project documents: it can be Vision, Meeting Minutes, Goal/feature model, etc. In analysis, do use graphical Use-Case models. Expand them into detailed textual scenarious once the diagrams are agreed upon with the customer.
In fact all that is rather simple once the team gets used to it.
Ok that's all for now, if you have any questions, feel free to ask.