Collider that can trip triggers that doesn't affect game physics?

I want to have some objects collide with a trigger. I could use a standard box collider but that effects collisions with the world and other objects. I don’t want the collider to effect physics in any way, but still collide with the trigger. Is this possible and how?

edit: This is the code I have to detect collisions. I have this script attached to a box collider. I want the units I have tagged as enemy to collide with the trigger and get destroyed. The problem is that I can’t use a standard box or sphere collider for the enemies because they have a big AI pathfinding script attached to them to control movement and adding a standard collider to them breaks their movement. They do have character controller attached to them so I am trying to collide with that.

function OnTriggernEnter (col : ControllerColliderHit)
{
	if (col.gameObject.tag == "Ground Enemy" || col.gameObject.tag == "Air Enemy")
	{
		Debug.Log("enemy destroyed");
		Destroy(gameObject);
	}
}

You have a typo above (TriggernEnter) so that might be affecting your testing; otherwise, just use layers per the doc

Search UA/Google for hundreds of examples, tuts, Q&A, etc.