We got some complaints that our App would continuously run-- pressing the ‘Home’ key does not quit the application. We had to add in a ‘Quit’ button to fix this (for those who develop on the iPhone, this is not allowed because it is against the developer docs).
Aye, this is fairly common for a lot of games that I’ve seen for Android. Angry Birds does something similar. A common solution that I’ve seen is to quit the game from the main menu if they press the “back” button. Once I got used to it, I actually appreciated it since I could hit “home”, do some stuff, then come immediately back to where I left off in the game.
I also like that the iphone pauses the game upon screen lock and home button press. The results vary on Android.
HOME button should not quit the app, but pause it. If you really want to quit at that point you can put a call to Application.Quit() in your OnApplicationPause function. Generally it’s not a problem with applications being put to the ‘background’ (like when pressing HOME); they consume next to no CPU and if the device runs low on memory the app will be killed.
Also, adding a ‘Quit’ button is not very Android’y; instead use the BACK button (KeyCode.Escape) for this.
A quit button in the main menue is not uncommon and no problem, sometimes they are also in the in game menue.
But if you close your app when I press the home button to multitask, you’ll get a lot of complaints, I’ll always contact the devs when they try to take away my multitasking. 
Thanks erique–
I don’t even have an iPhone or an Android, so I don’t get to notice what other apps are doing. I’ll take your advice and do just that. I mainly posted this because I moved from iPhone to Android, in which case ‘Home’ means quit (unless your on iPhone 4, in which case I have no idea what it does).