To add one that I haven't heard - I hate it when you slightly miss pressing on an ICON and it brings up the search screen. I don't want to bring up search screen. Do nothing when I miss - don't bring up the search screen.
I also want to be able to truly delete apps I've purchased or gotten from App store. Not that I'm embarrassed but things like old Olympics apps and similar that I just don't want to see when I looked at purchased apps. I'd be more willing to try apps if I could truly delete them from my account.