I've been using DOORS for a long time. The software does work and will help you manage your requirements. DXL makes it customizable and helps DOORS adapt to whatever processes your company has in place.
DOORS is the leading RM tool and for good reason. However, the software itself is long in the tooth. The UI conventions are pretty poor, you must invest in training, and the tool is really expensive, meaning that it's not for smaller shops.
I wish the tool was more "modern" in look, feel, and features. It lacks things like a dashboard interface, and the web interface is an expensive add-on (why?). You really need an expert to get the most out of the tool.
Still, despite its shortcomings, DOORS is a great tool and properly used it can help almost any project get a handle on requirements. But it's pricey and requires an expert/consultant to get the most out of it.