I remember having those thoughts and feelings when I got to my goal as well. At that point, I added in a couple hundred calories to approximate what I thought was maintenance level and set my new goal as a body fat % goal, not a weight goal. Some also set fitness goals (achievements; I did that a couple times as well). It worked very well; my body kind of settled into a new, comfortable weight that was actually between 5-10 pounds lower than goal. I did both cardio and weight training.
Maintaining is a challenge, and one I'm not doing gracefully (sidetracked by injuries, job change, and embarrassing lack of willpower), but that doesn't have anything to do with the time right after I hit goal, though...I did it, dropped, and maintained the lower weight for 2 years, and am now working to get back down to it, because it is a comfortable weight for me.