As a general rule, I'd always advocate explicitly calling the Dispose method for any class that offers it, either by calling the method directly or wrapping in a "using" block.
Most often, classes that implement IDisposible do so because they wrap some unmanaged resource that needs to be freed. While these classes should have finalizers that act as a safeguard, calling Dispose will help free that memory earlier and with lower overhead.
In the case of the Form object, as the link fro Kyra noted, the Close method is documented to invoke Dispose on your behalf so you need not do so explicitly. However, to me, that has always felt like relying on an implementaion detail. I prefer to always call both Close and Dispose for classes that implement them, to guard against implementation changes/errors and for the sake of being clear. A properly implemented Dispose method should be safe to invoke multiple times.