<p>Does having several levels of base classes slow down a class?  A derives B derives C derives D derives F derives G, ...</p>

<p>Does multiple inheritance slow down a class?</p>

If there are no virtual functions, then it shouldn't. If there are then there is a performance impact in calling the virtual functions as these are called via function pointers or other indirect methods (depends on the situation). However, I do not think that the impact is related to the depth of the inheritance hierarchy.
Brian, to be clear and answer your comment. If there are no virtual functions anywhere in your inheritance tree, then there is no performance impact.