I would simply like the ability to close an app vs. minimizing an app at the time that I'm leaving the app. Ideally, pressing the Home button would close the app I'm in, like it always did before. But I could double-tap Home to switch to another "running" app (or just click the home screen area), to leave my app without shutting it down. I cannot stand that the only way to truly close an app now involves so many clicks. It's tedious having to manage my phone like a poorly designed computer.
And to people saying I should contact the app makers.. most of the apps I want to close, not minimize, are Apple apps.. the ones built-in to my phone. I hate that the stock-ticker is slower to refresh now compared to when it always rerfeshed the instant it launched. I hate that settings don't start out at the root level every time I open them now, making it take more steps to navigate to where I wanted. I hate that the email app runs in the background, checking for messages, wasting my battery, cpu, and bandwidth, unless I manually kill it. I hate that the texting app restores exactly where I was, with the stupid keyboard still blocking my entire screen; because there is no button to collapse the keyboard, I used to exit/re-enter the app to hide it, but that workflow is broken now.
I don't think that people who wanted multi-tasking are whining now that it's here. Not just because it's here. We're whining because of how poorly it was implemented. Seriously, Microsoft did a better job in regards to multi-tasking and window-management with Windows 3.11 over 15 years ago. This is the worst UI design I've seen from Apple. Ever. It's pitiful.
A) At the time of wanting to leave an app, I should be able to easily close it or minimize it using a similar number of keystrokes. I should not have to (1) tap Home to minimize, (2) double-tap Home to bring up my task bar, (3) scroll to its icon, (4) hold down the icon to make it wiggle, (5) tap its X to close it for real, and (6) tap out to leave the task bar.
B) Apps which don't really run in the background or support any kind of quick re-launch should not stay in my task bar, even if I "minimize" them. An icon's presence in the taskbar should be indicative that it's still running, or cached, or otherwise in a state which is meaningfully different than "not running." An app with no multi-tasking support should never be in the taskbar. Period. Duh.
C) I would like a per-icon indicator on the taskbar which tells me how much of my resources a "minimized" app is using so that I know when it continues to use my bandwidth, cpu, ram, or battery in the background. I have no obvious way of identifying which apps are engineered well, and to make sure a rogue isn't churning my resources when I'm not using it, I end up closing all my apps all the time just to be safe. That defeats the entire point of multi-tasking.