Note: Favorites have since been renamed "Bookmarks". In addition, you can now follow a post, which is different from bookmarking as it’s something that’s completely private and gives you more notifications about activity.
Favorites are completely public. At any point in time you can see what a user's favorites are by searching
infavorites:#####, where the second part is their user id. (You can also use infavorites:mine as a shortcut to see your own favorites.)
There is not a way to see a list of people who favorited a certain question easily from the actual site interface. However the information is available via the Data Explorer (note that the information there is only updated once every week, on Sunday). If you know SQL, you can write your own queries there, otherwise there are several existing queries that will find the information you need, such as the following query (linked to in this main meta FAQ):
DECLARE @PostId int = ##PostId##
SELECT a.Id As [User Link], a.Reputation, b.CreationDate As DateFavorited
FROM USERS a, VOTES b WHERE b.UserId = a.Id AND b.VoteTypeId = 5 AND b.PostId = @PostId
ORDER BY b.CreationDate DESC
As for why this functionality is not available in the actual interface, I don't know. Adam Lear, in the 2012 Math Meta post linked to by MetaEd only said that this is "by design".
(In my opinion, being able to see each other's favorites is unnecessary. Personally, I don't like the idea of anyone and everyone being able to see my favorites, so I don't use the favorite feature.)