Should I update my apps on iPhone 4s? I have an iPhone 4s. I am not updating to IOS 8 as I have read enough warnings not to do this. All my apps now want to be updated, but most of those updates say that they are for IOS 8 compatibility. Should I do these updates? Will the apps still work normally for me?
Yes, you should continue to update your apps. Just because iOS 8 compatibility has been added to an app doesn't diminish the compatibility with earlier versions of iOS.

If an app has been updated to support iOS 8 and has removed support for iOS 7, you will not be given the option to update in the first place, however this is rare.