Why won't any of my apps open on my iPhone 4 i don't want to delete them and re install them any other ideas?

First thing you can do : restart the iphone

if that doesn't work: connect it to your computer and open iTunes.

There you can try to do an update (if there is one).

if that doesn't work either, go back to your iphone. click twice on the home button,

the multitask bar will appear and tap on one of the apps in that multitask bar. Tap it for some seconds until all apps in the bar start moving. You can now "delete" this apps from the multitask bar , this will not delete them from your iphone !

Maybe your RAM memory is full, and then a cleanup of your multitask bar can be a solution