Swiped from http://www.imdb.com/title/tt0361748/faq#.2.1.11:

Tarantino commented on "The Late Show" that Inglourious Basterds is the "Tarantino way of spelling it," but he hasn't commented on where the idea for the misspelling arose. Two theories have been offered by viewers. One theory is that "basterds" may be derived from the word "baster," a Dutch word for "bastard" meaning "crossbreed". In the movie, the "basterds" are American/Jewish. The original "Basters" were mainly persons of mixed descent between the Cape Colony Dutch and indigenous African women who at one time would have been absorbed in the white community. In the movie, the Basterds' plan was very similar: to be "civilians absorbed" in France, walking among the Nazis. In the film itself, the words are briefly shown in their misspelled form on Lt Aldo Raine (Brad Pitt)'s rifle. Near the end of the movie, Raine tells Col. Landa (Christoph Waltz) that his family grew up as backwoods bootleggers and moonshiners. Consequently, a second theory is that the misspelling is supposed to connote that Raine has had little in the way of schooling.