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When to save SharedPreferences?

I want to save some small data structures (~1kB total), as well as the user's preferences, while my app is closed. The settings are modified only in my PreferenceActivity, but the data structures are modified in pretty much every activity. I've extended Application and made all the data structures and preferences static. I've then tried saving to SharedPreferences in my application class's onTerminate() and loading it again in onCreate(). However, onTerminate()'s documentation states that "It will never be called on a production Android device, where processes are removed by simply killing them".
Answers to this question suggest saving to SharedPreferences in the onStop() method of each activity modifying their data. Will this guarantee that the data is saved in all cases? Is there a way to avoid the waste of saving every time the user transitions between activities (or should I even care)?

I would honestly just save in the onPause() of each activity as is recommended by Android (i.e. when you write an email notice how the draft is saved when the app pauses, such as if the screen turns off). Unless you notice that it is causing lags/delays, it probably won't matter too much.
If you do notice lags with this "autosave" method, then you should probably have some sort of "Save" functionality implemented in each activity, which could, for example, entail using a ProgressDialog / AsyncTask combination.

"persistent state" vs. "current state"

Attempting to decide (for my application) what to save in onPause() and what to save in onSaveInstanceState(), I combed the entire SO for hints and clear guidelines.
If I understand correctly, onSaveInstanceState() is best for saving "runtime changes" or "current state" (whatever that means), while onPause() is best for saving "persistent state" (whatever that means).
I am still having difficulty deciding what in my application constitutes "persistent state" vs. "current state". For example, while user preferences are clearly persistent, do I need to save them in onPause() when they are always saved automatically by the Android UI framework when the user changes them?
Do class data members need to be saved in onSaveInstanceState()? Do I need to do that for every class in my application?
I am confused.
Can you bring real-world examples of what must be saved in onPause() and what must be saved in onSaveInstanceState()? Except for device configuration changes, that is.
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Some new insights, after my question has been answered:
onSaveInstanceState's Bundle is not written to anything, and it's not persistent in any way.
onSaveInstanceState's Bundle data will only be held in memory until the application is closed.

You do not need to store user preferences in onPause because as you say, the framework does that for you.
To distinguish between persistent data vs state information, think of a text editor application.
Persistent data
Let's say the user has typed a couple words and then exits the app. The user didn't explicitly tell us to save that data to a file, but it sure would be nice to store that data away for when they come back. This is persistent data and you want to store it away in onPause().
State data
Similarly, say you have 2 tabs and a variable that tracks which tab is currently selected. This is state data that you'd store in onSaveInstanceState().
Gray matter
Finally imagine you have a class in the editor that keeps track of the number of characters and number of lines in the editor. This is state data, you could store it in onSaveInstanceState() or you can throw it away and simply recalculate it when you start up again. Whether you throw it away might depend on how long it takes to calculate, for instance if you could prevent a network request by storing data, do so.
Further thoughts
By playing with your app it should be obvious if there's an area where you failed to squirrel the right data away. Be sure to do things like hit the home button and then close out your app from the device manager. This will let you hit the corner cases where your app is shut down rather than just paused.
If your UI state is consistent across lifecycle events and your user data remains, good job.
Edit based on comment
I think there are 2 pieces of criteria here to determine when/what to save.
The first is quite subjective - Do you want to save data at all? There's truly nothing forcing you to save state or data. Will saving this information make for a better user experience? If you are writing an email and trying to copy/paste text from another app, losing your half typed email every time the app gets closed would be frustrating.
The second piece, determining what to save depends on whether you can reconstruct your UI state based on the data that you have. For instance, if you have saved text data then that must mean that the user was editing text. So now we know to switch to the edit text tab and fill in the saved text.
Generally speaking, if the desire is that you want to return the user to the same place they left off then you need to think about the state data required to get back to that point. Imagine a pristine loaded version of your app
what data needs to change to turn that into the last state the user
saw?
what data do you need to store to get back here?
This is really how android works, your activity is destroyed and recreated and it is your job to set the pieces in motion again (if you choose to do so).

Here is answer. You can save state in three different ways.
1) Subclassing app (not a good idea).
2) SharedPreferences (good for simple data, quick and reliable)
3) SQLite Database (More complex, also reliable).
Now to answer your question. There are really NO guarantees with android. At any time it can and may destroy your application without calling any particular function before it does so. So if there is data that is vital to save, the answer is save it as soon as you get it. There is usually not much advantage to saving something later, if you know you are going to need something save it immediately.
onSaveInstanceState() is just for saving temporary variables related to layout or orientation changes.
In summary persistent state/data (that should survive a crash), should be saved ASAP, don't wait for onPause(), because there are no guarantees. That's the reality.

The case I have is a game, where I want to save persistant data to a gameserver.
As this may take awhile, I find it not a good thing to try and save in onPause, but rather in onStop.
According to the tests I have done, onStop seem to be able to run in the background while onPause blocks, atleast that is the case when I press home (tested with a simple for 1 to 10m loop in onPause and onStop).
Can anyone confirm this blocking theory ?
onStop NEEDS Honeycomb up (api11+), because before that version you can get killed before onClose is called.
See here and look for killable in the table - If reality matches the documentation is another question :).

Save android activity state

I try to create LUDO game and when user stop the game I want to save game state (Activity state).
I understood that I need to save state in method OnPause() but there are lots variables that I need to save and there are all changing in time so I am not sure that I can save state in that way.
So can I save the whole Activity and OnResume() method to restored it and just continue whith the game?
Thanks.

Don't know what you mean by changing in time. Are you saying your game progresses even while the player isn't playing? Normally, you would save only the minimum amount of information necessary to recreate the current state. For a board game, this could be the locations of each players' pieces, and whose turn it is.
If you really have so much game state that it would be unwieldy to save and restore, or the game has to progress while the Activity is closed, or recreating the state from static data is too difficult (all propositions I would probably dispute, but we can take it a given for the sake of discussion), then I would suggest you write it as a client-server app, where an Android Service runs the game engine and your Activity does all the visuals and user interaction.

I think you are looking for How to save an Android application's state.
The documentation also provides details on saving persistent state with onPause.

Android - saving application state

I want to save application state to be able to restore it after another launch. Is is it better to use method onSaveInstanceState and save it to Bundle or to use SharedPreferences?
Thanks

It depends on your intention. Using the onSaveInstanceState() is only a reasonable solution if you want to ensure saving the state during configurations changes and other restarting events. In case you aim for a true saving of the application's state beyond the lifecycle of the application, you should consider using either the SharedPreferences or maybe even employ a database.

I may not have the same development chops as some of the other posters here (I've been seriously developing apps since July 2012), but I've found a solution that integrates SharedPreferences as well as the onSaveInstanceState().
My App has a splash screen activity that reads values from SharedPreferences and assigns them to the appropriate variables. Additionally, each Activity I make has its own onSaveInstanceState() method, and I commit all of the data I need to save to SharedPreferences there, in each and every Activity. Since onSaveInstanceState() is run before an App or Activity closes normally, it should back up data values under all normal circumstances.
It may not be the most code-efficient solution, especially in larger Apps with many Activities, but as far as my tests go it protects your app from data loss 99% of the time.
If a more experienced developer would like to chime in and confirm or deny this, I'm sure it'll enrich the question and answer.

I am sure onSaveInstanceState() is the better option.
Here it is already given a better explanation: Saving Android Activity state using Save Instance State

How to store state in an Android Service

I'd like to make my IntentService remember when it was called last time and how many times it was called so far. It doesn't matter if these values are reset when the phone is rebooted, but they must not be reset when the application process is killed.
Should I store these state variables in a SharedPreferences, or is there is a better and/or more lightweight way? I tried intent.getExtras(), but it seems that the values I put there are not remembered between calls.

For persistent storage like this, SharedPreferences is usually the way to go. And don't forget to do commit() after editing the preference.