Is there a unique Android device ID?

Settings.Secure#ANDROID_ID returns the Android ID as an unique 64-bit hex string.

import android.provider.Settings.Secure;

private String android_id = Secure.getString(getContext().getContentResolver(),
                                                        Secure.ANDROID_ID); 

There are many answers to this question, most of which will only work "some" of the time, and unfortunately that's not good enough.
Based on my tests of devices (all phones, at least one of which is not activated):
All devices tested returned a value for TelephonyManager.getDeviceId()
All GSM devices (all tested with a SIM) returned a value forTelephonyManager.getSimSerialNumber()
All CDMA devices returned null for getSimSerialNumber() (as expected)
All devices with a Google account added returned a value for ANDROID_ID
All CDMA devices returned the same value (or derivation of the same value) for both ANDROID_IDand TelephonyManager.getDeviceId() -- as long as a Google account has been added during setup.
I did not yet have a chance to test GSM devices with no SIM, a GSM device with no Google account added, or any of the devices in airplane mode.
So if you want something unique to the device itself, TM.getDeviceId() should be sufficient. Obviously some users are more paranoid than others, so it might be useful to hash 1 or more of these identifiers, so that the string is still virtually unique to the device, but does not explicitly identify the user's actual device. For example, using String.hashCode(), combined with a UUID:
    final TelephonyManager tm = (TelephonyManager) getBaseContext().getSystemService(Context.TELEPHONY_SERVICE);

    final String tmDevice, tmSerial, tmPhone, androidId;
    tmDevice = "" + tm.getDeviceId();
    tmSerial = "" + tm.getSimSerialNumber();
    androidId = "" + android.provider.Settings.Secure.getString(getContentResolver(), android.provider.Settings.Secure.ANDROID_ID);

    UUID deviceUuid = new UUID(androidId.hashCode(), ((long)tmDevice.hashCode() << 32) | tmSerial.hashCode());
    String deviceId = deviceUuid.toString();
might result in something like: 00000000-54b3-e7c7-0000-000046bffd97
It works well enough for me.
 
 
Also you might consider the WiFi adapter's MAC address. Retrieved thusly:
WifiManager wm = (WifiManager)Ctxt.getSystemService(Context.WIFI_SERVICE);
return wm.getConnectionInfo().getMacAddress();
Reported to be available even when WiFi is not connected. If Joe from the answer above gives this one a try on his many devices, that'd be nice.