I'm not a very good player and so I don't really take notice of the stars - unless, of course, it's for a contest when I need a specific number of stars.
Those stars only important when I want to replay back certain levels, because I think basically 3 stars means easier to pass the levels and 1 star is hard.
I always try for three stars but wish you got something for the more starts you get and something a little extra when you get so many in a row. I think that would be a good extra incentive.
You don't really have control about how many stars you get when passing a level. It's good to get stars but sometimes passing a SUPER HARD LEVEL you only get one star. Seems to me the harder the level the more stars you should get.