Easy. Apps which save their state when you close them. Not a solution to all problems (i.e. playing music in the background) but to the user it doesn't make any difference whether that Spreadsheet app she just left to take a note keeps on running in the background or quits if she finds it exactly the way she left it when coming back. (As long as it's speedy enough.)

Users don't want multitasking. They may say so - don't listen to them. They want to be able to do stuff. One traditional way to let them do stuff is multitaksing. That's why they are screaming for it now. But there is no reason why the solution that let's them do stuff actually has to be multitasking. It could be something else entirely.