Java's HashMap class extends the Serializable interface, which makes it easy to add it to an intent, using the Intent.putExtra(String, Serializable) method.
In the activity/service/broadcast receiver that receives the intent, you then call
Intent.getSerializableExtra(String) with the name that you used with putExtra.
For example, when sending the intent:
HashMap<String, String> hashMap = new HashMap<String, String>();
hashMap.put("key", "value");
Intent intent = new Intent(this, MyOtherActivity.class);
intent.putExtra("map", hashMap);
startActivity(intent);