Abusing reflection and the internal Unity player build error function to get stacktrace-less error logs. Not recommended for anything sane.

TerriblyHackyLog.cs

using UnityEngine;
using System.Reflection;

public class TerriblyHackyLog : MonoBehaviour
{
	void Start ()
	{
		Log ("Aaaaarrrrgh!");
	}


	static void Log (string message)
	{
		typeof (Debug).GetMethod (
			"LogPlayerBuildError",
			BindingFlags.Static | BindingFlags.InvokeMethod | BindingFlags.NonPublic
		).Invoke (
			null,
			new object[]{message, "", 0, 0}
		);
	}
}