Most Americans (except for those residing in northwest New York state), have indeed forgotten about the War of 1812. Some might recall the White House getting torched. Growing up I always sort of thought of it as a war at sea, with the stunning American victories over the Royal Navy being the highlights: USS Constitution vs. HMSs Java and Guerriere, USS United States vs. HMS Macedonian, the Battle of Lake Erie, etc. I was never very clear on the land actions.
Of course, there was that popular song about the Battle of New Orleans! "In 1814 we took a little trip...."