The War of 1812 was, in many ways insignificant. The issues to resolve were left over from the Peace of Paris, ending the Revolution and the most important battle didn't take place until after the peace treaty had been signed.
Hostilities lasted from 1812 through 1815. There were few occassions where the opposing forces managed to meet each other on the battlefield until the Battle of New Orleans. Up until this time, the majority of the damage was done by burning cities in their wake. (This is when Washington, D.C. was burned, and also Buffalo, New York.) I don't want to give the impression that there were no battles other than the Battle of New Orleans, but all in all, they were relatively minor.
The Battle of New Orleans is unique in that it was the most important battle of the War of 1812 and that it took place after the peace treaty, the Treaty of Ghent, was signed. (News hadn't reached Andrew Jackson's forces of the signing of the peace.)
If one of your ancestors was born between 1762 and 1797 it might be worth looking to see if they were involved in the War of 1812.
Here are some related links:
1812
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David Nevin / Hardcover / Published 1996
1812
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David Nevin / Mass Market Paperback / Published 1997
1812 : A Novel
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David Nevin, Dick Hill (Narrator) / Audio Cassette / Published 1996