Thought I'd add some parties that I had as a kid!
I loved sleepovers as a girl...had them almost every year from when I was 9-14? of course, at 9 it was different than at 14. i think one of the best money ideas is to give your kids a budget. for younger kids, give them an item number limit. for example;
3 bottles of soda
2 bags of chips
one dip
2 types of candy
etc...this way, they get to be involved, and if they shop with you they see how much stuff you are actually buying for the party.
when i was younger my mom always planned a craft to do...
once we all got teddy bears, and had cloth, little staw hats, lace, etc to decorate and make outfits. i think this was maybe my 9th birthday...we still have a picture and we all look so happy holding up our bears

i think she bought the bears on sale at a craft store, and bought cheap lace/ribbon/fabric from clearance sections...we thought it was so fun desiging the outfits that we didnt care what the fabric looked like!
one year we did hair bows...you took a piece of plastic, folded it over, hot glued two sides, we all filled the plastic with sequins/beads/etc, then the adults glued the last side, i think gathered the center with a bow, and glued a barette thing to the back.
we also put on shows and made up dances, just for fun. i think the american idol idea is great, but maybe switch it around a bit so the more shy girls don't feel left out...have a movie making party, give the kids stuff for costumes (goodwill) and they can use props from around the house. they could also do a play, and you could give all of the parents a time to come back so the kids have an audience.
just some ideas...i've seen them all work well! of course, i think one of my faves was when i turned 15...i told my mom no presents, i just want to go to disney! well we did it very cheaply and i was able to bring a friend for a day....so fun!
i also had gymnastics birhday parties...those were really cool too! whatever your child wants to do, there are ways to do it on a budget (i've realized this while working a summer camp!) have fun!