Running multiple AsyncTasks at the same time -- not possible?

This allows for parallel execution on all android versions with API 4+ (Android 1.6+):

@TargetApi(Build.VERSION_CODES.HONEYCOMB) // API 11
void startMyTask(AsyncTask asyncTask) {
    if(Build.VERSION.SDK_INT >= Build.VERSION_CODES.HONEYCOMB)
        asyncTask.executeOnExecutor(AsyncTask.THREAD_POOL_EXECUTOR, params);
    else
        asyncTask.execute(params);
}

This is a summary of Arhimed's excellent answer.

Please make sure you use API level 11 or higher as your project build target. In Eclipse, that is Project > Properties > Android > Project Build Target. This will not break backward compatibility to lower API levels. Don't worry, you will get Lint errors if your accidentally use features introduced later than minSdkVersion. If you really want to use features introduced later than minSdkVersion, you can suppress those errors using annotations, but in that case, you need take care about compatibility yourself. This is exactly what happened in the code snippet above.

Update 2022

Note that AsyncTasks got deprecated quite a while ago. If you use Kotlin, it is recommended to use Kotlin Coroutines and if you depend on using Java in your project, an alternative is to use Executors from java.util.concurrent. (source)

Making @sulai suggestion more generic :

@TargetApi(Build.VERSION_CODES.HONEYCOMB) // API 11
public static <T> void executeAsyncTask(AsyncTask<T, ?, ?> asyncTask, T... params) {
    if(Build.VERSION.SDK_INT >= Build.VERSION_CODES.HONEYCOMB)
        asyncTask.executeOnExecutor(AsyncTask.THREAD_POOL_EXECUTOR, params);
    else
        asyncTask.execute(params);
}   

Just to include the latest update (UPDATE 4) in @Arhimed 's immaculate answer in the very good summary of @sulai:

void doTheTask(AsyncTask task) {
    if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.KITKAT) { // Android 4.4 (API 19) and above
        // Parallel AsyncTasks are possible, with the thread-pool size dependent on device
        // hardware
        task.execute(params);
    } else if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.HONEYCOMB) { // Android 3.0 to
        // Android 4.3
        // Parallel AsyncTasks are not possible unless using executeOnExecutor
        task.executeOnExecutor(AsyncTask.THREAD_POOL_EXECUTOR, params);
    } else { // Below Android 3.0
        // Parallel AsyncTasks are possible, with fixed thread-pool size
        task.execute(params);
    }
}

AsyncTask uses a thread pool pattern for running the stuff from doInBackground(). The issue is initially (in early Android OS versions) the pool size was just 1, meaning no parallel computations for a bunch of AsyncTasks. But later they fixed that and now the size is 5, so at most 5 AsyncTasks can run simultaneously. Unfortunately I don't remember in what version exactly they changed that.

UPDATE:

Here is what current (2012-01-27) API says on this:

When first introduced, AsyncTasks were executed serially on a single background thread. Starting with DONUT, this was changed to a pool of threads allowing multiple tasks to operate in parallel. After HONEYCOMB, it is planned to change this back to a single thread to avoid common application errors caused by parallel execution. If you truly want parallel execution, you can use the executeOnExecutor(Executor, Params...) version of this method with THREAD_POOL_EXECUTOR; however, see commentary there for warnings on its use.

DONUT is Android 1.6, HONEYCOMB is Android 3.0.

UPDATE: 2

See the comment by kabuko from Mar 7 2012 at 1:27.

It turns out that for APIs where "a pool of threads allowing multiple tasks to operate in parallel" is used (starting from 1.6 and ending on 3.0) the number of simultaneously running AsyncTasks depends on how many tasks have been passed for execution already, but have not finished their doInBackground() yet.

This is tested/confirmed by me on 2.2. Suppose you have a custom AsyncTask that just sleeps a second in doInBackground(). AsyncTasks use a fixed size queue internally for storing delayed tasks. Queue size is 10 by default. If you start 15 your custom tasks in a row, then first 5 will enter their doInBackground(), but the rest will wait in a queue for a free worker thread. As soon as any of the first 5 finishes, and thus releases a worker thread, a task from the queue will start execution. So in this case at most 5 tasks will run simultaneously. However if you start 16 your custom tasks in a row, then first 5 will enter their doInBackground(), the rest 10 will get into the queue, but for the 16th a new worker thread will be created so it'll start execution immediately. So in this case at most 6 tasks will run simultaneously.

There is a limit of how many tasks can be run simultaneously. Since AsyncTask uses a thread pool executor with limited max number of worker threads (128) and the delayed tasks queue has fixed size 10, if you try to execute more than 138 your custom tasks the app will crash with java.util.concurrent.RejectedExecutionException.

Starting from 3.0 the API allows to use your custom thread pool executor via AsyncTask.executeOnExecutor(Executor exec, Params... params) method. This allows, for instance, to configure the size of the delayed tasks queue if default 10 is not what you need.

As @Knossos mentions, there is an option to use AsyncTaskCompat.executeParallel(task, params); from support v.4 library to run tasks in parallel without bothering with API level. This method became deprecated in API level 26.0.0.

UPDATE: 3

Here is a simple test app to play with number of tasks, serial vs. parallel execution: https://github.com/vitkhudenko/test_asynctask

UPDATE: 4 (thanks @penkzhou for pointing this out)

Starting from Android 4.4 AsyncTask behaves differently from what was described in UPDATE: 2 section. There is a fix to prevent AsyncTask from creating too many threads.

Before Android 4.4 (API 19) AsyncTask had the following fields:

private static final int CORE_POOL_SIZE = 5;
private static final int MAXIMUM_POOL_SIZE = 128;
private static final BlockingQueue<Runnable> sPoolWorkQueue =
        new LinkedBlockingQueue<Runnable>(10);

In Android 4.4 (API 19) the above fields are changed to this:

private static final int CPU_COUNT = Runtime.getRuntime().availableProcessors();
private static final int CORE_POOL_SIZE = CPU_COUNT + 1;
private static final int MAXIMUM_POOL_SIZE = CPU_COUNT * 2 + 1;
private static final BlockingQueue<Runnable> sPoolWorkQueue =
        new LinkedBlockingQueue<Runnable>(128);

This change increases the size of the queue to 128 items and reduces the maximum number of threads to the number of CPU cores * 2 + 1. Apps can still submit the same number of tasks.