Soaps will have many different directors and some drama series have more than one director (probably depends a bit on the length of the series) - but other drama series do often have the same director. For the leads I think the final decision will always be the producer - producers can over-ride a director's wishes sometimes.
On the rare occasions I've been seen for TV I have always met the director - either of the one-off drama or the particular episode of a soap. I've never been seen for a lead role though
Directors don't always have the final say in films I don't think. The producer will be king-pin there too - especially when it comes to the casting of "names".
