Genre can hold multiple values, but it's not designed to be edited as a multi-value field. I'm not sure why, since this functionality definitely exists in Media Center.
You can easily assign to multiple Genres, but it's a manual process. If you want to assign the Genre values of Action and Thriller, do it like this:
Action;Thriller
If this is something you are going to do a lot, I would recommend creating a new field called [Genres] . Make it a string type, but make it's edit type "List", instead of "Standard". That way you can do checkbox assignment with multiple values making things easy, and less error prone. With the stock Genre field, you will have to type out the Genre names.
You can also do it with Pane Tagging, but I find that to be kind of clunky. I'd rather do it with the Tag Action Window and a List edit type personally.
Brian.