In .NET the garbage collector will automatically free memory when an object can no longer be referenced from anywhere. When it does so, if the object has a finalizer it calls the finalizer. The finalizer is for cleaning up, usually unmanaged resources.
However, finalizers are expensive (they delay garbage collection on an object, for example) and you cannot tell when it will be run (as you can't tell when the GC will decide to collect it). They are usually left as a last resort for cleaning up things like unmanaged resources.
This is where the IDisposable interface and it's Dispose method comes in. Dispose can also be used to clean up, both managed and unmanaged resources. When you call the Dispose method it cleans up and the object is no longer in a stable, usable state.
If you have a resource which implements IDisposable you can call Dispose on it when you know you are done. That way and resources it is holding on to can be freed up as soon as possible. The usual way of doing this is to wrap it up in a using statement, which will automatically Dispose when the using block is done. e.g.:
using (SomeDisposableObject disposableObject = new SomeDisposableObject())
{
disposableObject.DoSomeStuff();
disposableObject.DoSomeMoreStuff();
}
When the using block is finished (after DoMoreStuff) Dispose is called on disposableObject. Using statements are a lot cleaner than the equivalent code when you take into account exception handling.
In the case of something like ToolTip, which has unmanaged references (a lot of WinForms in a wrapper around the unmanaged Win32 components) it will have a finalizer to make doubly sure the unamanged resources are freed correctly. However, if you call Dispose on the object, the cleanup code is run there and then and the finalizer is suppressed (it won't run when the object is collection by the GC).
So, to answer your question more directly, if you know exactly when an IDisposable is finished with it is a good idea to call Dispose. However, if you don't it is usually ok just to leave it up to the garbage collector to collect it and call the relevant code to correctly cleanup the object.
In the cases of ToolTip and Timer given, I wouldn't worry about calling Dispose on them yourself as I suspect it would be difficult to predict when they will be finished with.