Can't think of any where a unit was completely destroyed, but a few instances where it came close was the initial Chinese entry into the Korean War. In these cases there were generally survivors but often the unit would be so decimated that it ceases to exist:
During the US 8th Army retreat from the Chongchon River:
"The 2d Engineer Battalion lost 711 of its original 977 men, along with more than 95 percent of its equipment. During the withdrawal, the 2d Division sustained such high casualties and equipment losses that it was out of action for several months. Only the arrival of the 1st Cavalry Division at Sunch'on saved the 2d Division from total annihilation."
At the Battle of Unsan, the 8th Cavalry regiment of the 1st cav division suffered huge losses incl over 1100 casualties. The 1st and 2nd Battalion slipped through encirclement by abandoning most of their equipment, whilst the 3rd battalion essentially ceased the exist, though some survivors escaped.
These are two of many examples during the first and second phase Chinese intervention into the Korean war.
edit: bah, how did I forget about that other great Native American victory?
Happened a little early, 1791, but something like 950 of the 1,000 strong militia and regular force of the US were casualties.
I assume you mean to exclude naval combat, as there would be quite a few instances of this if we were to include that.
USS Juneau springs to mind. She was a light cruiser sunk at the Battle of Guadalcanal, and while her entire crew was not lost with the ship, the nature of her sinking was such (she was cracked in half by two torpedoes), that the remainder of the US fleet assumed the crew were all dead and left to engage the remaining IJN fleet. Ultimately, only 16 of her original crew of 700 officers and men survived. This would be much larger than a standard company, and larger than many comparable Army battalions in WWII.
Interestingly, Juneau was the ship on which the Sullivan brothers were all stationed (five of them), which led, along with the deaths of the Bergstrom brothers, to changes in US armed forces policies toward sole survivors and the placement of family members in single units or aboard single ships.
The only two times that an entire unit of US Service Personnnel were wiped out to a man was the Custer fight, and in 1854, the annihilation of all 28 members of a unit under the command of a Lieutenant Grattan. Both of these events were the result of conflict with the Lakota (Plains Sioux) tribe.
Not exactly a company sized unit, but significant nonetheless.
http://en.wikipedia.org/wiki/Grattan_massacre
(edited for clarity)