At the battle of Guilford Courthouse, the American army deployed in a formation quite unlike those traditionally used by European armies. The American commander, Major-General Nathanael Greene, drew his men up in three successive lines that were designed to attrite the attacking British army. First, the British would be confronted by a line of North Carolina militia, then by a line of Virginia militia, and then finally by a line of Maryland and Virginia Continentals.
An obvious inspiration for this deployment was that used by Brigadier-General Daniel Morgan at the battle of Cowpens, 2 months earlier. However, Guilford Courthouse and Cowpens were hardly the first time that such a deployment was used during the war. A less elaborate version of this strategy was employed on numerous occasions, including at the battles of Long Island, White Plains, Brandywine, and Freeman's Farm. On each of these occasions, the Americans dispatched a strong force to wear down the advancing British before the British could attack the Americans’ main defensive line. On Long Island, for example, the advanced force was placed on a rocky, wooded spine well in advance of the American fortifications at Brooklyn. However, the British were able to outflank this force and inflict a major defeat on the Americans. Conversely, at Freeman's Farm the advanced American party brought the British advance to a standstill, and the main line was never seriously threatened.
The battles of Long Island and Freeman's Farm are relatively well known. Below is a description of how the Americans used this strategy at the lesser-known battle of White Plains, New York (October 28, 1776).
George Washington’s army entrenched at White Plains, New York, after having been driven from Manhattan. The British army advanced on his position in two columns. Washington detached a handful of regiments to harry their advance.
The party confronting the left British column included the 1st and 5th Connecticut State Battalions. At the head of the opposing British column was the 2nd Jäger company, the 3rd battalion of light infantry, and half of the 17th Light Dragoons.
In brief, the Americans used stone walls as impromptu breastworks from which they fired on the head of the advancing British column. The British then halted, brought up some field pieces, and fired on the Americans from outside of musket range. The Americans were finally forced to retreat when their flank was threatened. The advanced party prolonged the fight as long as it could, but unlike Cowpens or Guilford Courthouse, they were unable to inflict serious losses on the British. 
Here are several descriptions of this incident:
Colonel William Douglas (commander of the 5th Connecticut State Battalion):
I was ordered out with my regiment [and] with three others to meet and endeavor to retard their [the British] march. We moved on and at about twelve were attacked by their advanced guard. We drove them back but soon after the main body came on and we stood them until they got on our flank and I ordered a retreat. We had a most severe fire to retreat under, ten men to our one, but we came off in good order and very surely fired on our retreat all the way. I lost three dead and five wounded. They cut my regiment off from our main body and got ahead of me but I took advantage of a wood and got clear of them. 
Colonel Gold Silliman (commander of the 1st Connecticut State Battalion):
... Yesterday about 10 o'clock in the morning we had news that the enemy were approaching, when I with my regiment & 3 others were ordered out about 1 1/2 miles below our lines to take post on a hill to gall them in their march as they advanced. We accordingly took our post & mine & one other regiment had the advantage of a stone wall right in front at which we had been waiting but little time before the enemy came up within 6 or 8 rods,--when our men rose from behind the wall, poured in a most furious fire.
The enemy retreated & came on several times & were so hotly received every time that finally we drove them off from the hill. We killed some they did not carry off & some they did.
I had not one either killed or wounded. On this the enemy were coming upon us with a number of field pieces & as we had none there to meet them with, we were ordered to retreat over West on to another Hill [Chatterton's] & join another party of men & accordingly did it & formed a line of battle. 
Captain Johann Ewald (commander, 2nd Jäger Company):
The army had marched scarcely two hours when the left column encountered an advanced corps of the enemy, which I had to engage supported by the light infantry. The area was intersected by hills, woods, and marshes, and every field was enclosed with a stone wall. This enemy corps had taken a stand behind the stone walls on the steep hills between two plantations. Several guns were set up on the main road at some distance, which were covered by cavalry. General Heister [commander of the left British column] immediately mounted a battery on the main road and cannonaded the enemy, who withdrew to his own lines behind a creek with high banks and deployed upon the steep hills. 
1. The actions involving the 1st and 5th Connecticut State Battalions are fairly well described in the sources that I’ve encountered. Douglas’ and Silliman’s account suggest that there were other units on hand, but do not name them. As far as I’ve been able to deduce (my reading and research on this battle is not exhaustive), these two units were accompanied by Sage’s 3rd Connecticut State Battalion and Selden’s 4th Connecticut State Battalion, neither of which distinguished itself in this fight. The right British column was led by the 1st Jäger Company, half of the 16th Light Dragoons, and the 1st and 2nd battalions of light infantry (according to Ewald). At a minimum, some Pennsylvania riflemen were dispatched to resist their advance. There may have been other American units present too, but frankly I’m unsure (it is difficult to identify, for several American regiments reporting casualties, where those losses occurred).
As mentioned by Douglas, the British cut off the 1st and 5th Connecticut State Battalions from the American main line. Therefore, they retreated in a westerly direction (towards their right) and took up position alongside a hodgepodge of other American units on Chatterton’s Hill. The British left column was then sent to attack this position, and the subsequent assault is what is usually described when historians write about the battle of White Plains. (That is, the fight by the advanced parties has received comparatively little attention).
2. The Long Island Historical Society. (1878). The campaign of 1776 around New York and Brooklyn.
3. Joseph P. Tustin (1979). Diary of the American War: A Hessian journal. Captain Johann Ewald.