Well, the militia actually acquitted themselves fairly well against battle-hardened British regulars during the War of 1812, at least in the lower part of the United States. American operations against Canada, for both the militia and the regular Army, were much more hazy.
The war was, by and large, rather unpopular, especially in New England, whose seaborn trade was badly hurt by the war.
The Battle of Bladensburg is one instance in which the militia, in combination with some regular Navy forces, acquitted themselves fairly well against the British even though the ultimate results were a failure.
The American militia troops, including naval militia that had earlier harassed the British fleet in the Cheasapeake and in the rivers leading to the Chesapeake, held their own against assaults by several thousand British troops, but when they tried to take the initiatitive and drive the British back, the attack faltered through poor coordination and was broken, leaving the road to Washington open to the British.
American militia troops also helped blunt the British attempts to take Fort McHenry. The Battle of North Point saw the Maryland militia blunt the British land attempt to take Baltimore. The action also saw the death of British General Ross.
The true shining example of the American citizen's militia in the War of 1812 was at the Battle of New Orleans.
The battle included a small force of American regular army and about 2,000 to 3,000 local militia. Everyone who's heard Johnny Horton's song "The Battle of New Orleans" knows how it turned out -- fewer than 100 American casualties, nearly 1,500 British casualties, including the commanding general.
