If a music streaming app is running in the background, it should be obvious since you can hear it.
If a navigation app is running in the background, there will be the indicator in the status bar that indicates location or GPS services are being used.
Very few 3rd party apps actually run in the background or will run in the background after being updated for iOS4 - the overwhelming majority will continue to be quit or placed in a suspended state which aren't using processor cycles or battery.
In regards to a navigation app like TomTom, the following was copied from this link.
http://whenwillapple.com/blog/2010/04/19/iphone-os-4-multitasking-explained-agai n/
What happens when you’ve arrived and want to shut it off so it doesn’t drain the battery? No, you don’t need to manually task manage and force close. When you reach your destination and are no longer navigating, it will automatically stop using the background navigation and go into regular suspend mode when you leave the app. If you leave the app while still in navigation mode and disconnect from power, you’ll soon get a local notification popup asking if you would still like to navigate in the background. Tap no and send TomTom into suspend mode. You can always confirm that it is no longer running in the background by looking for the new GPS arrow icon (see picture below)…if it’s gone, it’s not navigating.
All 3rd party navigation apps that are updated to run in the background may not include the same which is up to the developer for the app, but any developer for such as app that is worth their salt will do so. If not, there will be the location services indicator in the status bar when such an app is running in the background.
+Q: How do you close applications when multitasking?+
+A: (Scott Forstall) You don’t have to. The user just uses things and doesn’t ever have to worry about it.+
+A: (Steve Jobs) It’s like we said on the iPad, if you see a stylus, they blew it. In multitasking, if you see a task manager… they blew it. Users shouldn’t ever have to think about it.+