How to get a list of the activity history stack?

So is there a way to do that using a function from the SDK?

No, sorry.

Would it be possible to listen to "start/finish activity" events with some kind of receiver to a specific app (mine) and keep track of the stack history?

You can use registerActivityLifecycleCallbacks() on Application, if you are only going to support API Level 14 and higher (a.k.a., Android 4.0+).

Using ADB commands:

adb shell dumpsys activity activities  # displays list of activities in back stack

adb shell dumpsys activity process  # displays list process in back stack

adb shell dumpsys activity intents  # displays list of pending intents in back stack

adb shell dumpsys activity broadcast  # displays list of broadcast in back stack

adb shell dumpsys activity services  # displays list of services running in back stack

Using Activity manager:

ActivityManager m = (ActivityManager) ctx.getSystemService( ctx.ACTIVITY_SERVICE );
List<RunningTaskInfo> runningTaskInfoList =  m.getRunningTasks(10);
Iterator<RunningTaskInfo> itr = runningTaskInfoList.iterator();

while(itr.hasNext()){
    RunningTaskInfo runningTaskInfo = (RunningTaskInfo)itr.next();
    int id = runningTaskInfo.id;
    CharSequence desc= runningTaskInfo.description;
    int numOfActivities = runningTaskInfo.numActivities;
    String topActivity = runningTaskInfo.topActivity.getShortClassName();
}