<p>Should I bind directly to objects returned from a webservice or should I have client-side objects that I bind to my gridcontrols? For instance if I have a service that returns object Car should I have a client side Car object that I populate with values from the webservice Car object? 
What is considered best-practice?
In C# do I need to mark my classes as serializable or do something special to them?</p>

This really depends on what you are getting from the web service. If they are simple data transfer objects and you are only displaying data, then yes, you can bind. If you plan to edit the objects, it may not be usefull as you will need to track changes.
Do your objects and/or collections on the client track changes? If so you can use them.
If you have no change tracking, then you will need to track changes yourself, so you may need to translate the objects or wrap them in something to track changes.
Again, it really depends on what you are getting, what they support, what you are doing with them, as well as what response the server wants back for changes.