From Wikipedia page on the film:-

The film's title was inspired by the English-language title of director Enzo G. Castellari's 1978 war film, The Inglorious Bastards. When asked for an explanation of the film's title's spelling during a news conference at the Cannes Film Festival, Tarantino said, "I'm never going to explain that".

When pushed on it, Tarantino would not explain the first u in Inglourious, but said, "The Basterds? That's just the way you say it: Basterds." Tarantino later stated in an interview that the misspelled title is "a Basquiat-esque touch."

He further commented on Late Show with David Letterman that Inglourious Basterds is a "Quentin Tarantino spelling".

Tarantino is famous for raising this kind of unanswered question to play with viewers mind.

From IMDB FAQ

Why is it spelled "Basterds"?

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, nor is he likely to. "I'm never going to explain that," Tarantino was quoted at the Cannes Film Festival.

Three theories have been offered by viewers.

1. Basterd may be derived from the word Baster, a word derived from Dutch bastaard (bastard). 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 are American/Jewish, and their plan was very similar...to be "civilians absorbed" in France, walking among the Nazis.

2. The misspelling may connote that Lt Aldo Raine (Brad Pitt), who grew up in a family of backwoods bootleggers and moonshiners, has had little in the way of schooling. The words are briefly shown in their misspelled form on his rifle.

3. Tarantino misspelled the title on the cover of the script, which then leaked onto the internet before production began. Rather than admit his mistake, Tarantino chose to maintain the spelling.

The above were merely audience opinions. But here's a promising article from RottenTomatoes where Weinstein Co. and Universal Pictures, confirms that QT is not a poor speller and gives the reasons for the title.

Inglourious Basterds begins in German-occupied France, where Shoshanna Dreyfus (Mélanie Laurent) witnesses the execution of her family at the hand of Nazi Colonel Hans Landa (Christoph Waltz). Shosanna narrowly escapes and flees to Paris, where she forges a new identity as the owner and operator of a cinema.

Elsewhere in Europe, Lieutenant Aldo Raine (Brad Pitt) organizes a group of Jewish soldiers to engage in targeted acts of retribution. Known to their enemy as "The Basterds," Raine's squad joins German actress and undercover agent Bridget Von Hammersmark (Diane Kruger) on a mission to take down the leaders of The Third Reich. Fates converge under a cinema marquee, where Shosanna is poised to carry out a revenge plan of her own...

Because they're from Bostin

It's spelled basterd because they're from Bostin and that's how they spell it there — or rather, how they pronounce it.

Unfilmed flashback

According to an article on Cracked.com, "6 Crucial Movie Scenes That Never Made It Out of the Script", this was explained in a scene that was scripted but never filmed.

It was a flashback to Boston, spelled "Bostin" in the script, where Donny buys a baseball bat and then goes around his Jewish neighbourhood, asking people if they have any loved ones in Europe they're concerned for and if they want to sign the bat for them.

INT - SPORTING GOODS STORE- DAY
MR.GOOROWITZ'S sporting goods shop in Donny's Jewish Bostin
neighbourhood. Donny walks in.

MR.GOOROWITZ
Hello Donny, how are you?

DONNY
Ah, just dandy, Mr.Goorowitz.

MR.GOOROWITZ
Your mother, your father - everything
good there?

DONNY
There just fine. I'm shippin off next
week.
The store proprietor, extends his hand to the young man.

MR.GOOROWITZ
Good for you son. Kill one of those
Nazi basterds for me, will ya?

DONNY
That's the idea, Mr.Goorowitz.

MR.GOOROWITZ
What can I do you for, Donny?

DONNY
I need a baseball bat.

He goes to a mrs. Himmelstein, who is about to sign it "Madeleine".

MRS.HIMMELSTEIN
You must be a real BASTERD, Donny?

DONNY
You bet your sweet ass I am.

MRS.HIMMELSTEIN
Good. A Basterds work is never done.
Specially in Germany.

We then see Donny beating Werner to death with that same bat.

Quentin Tarantino loves to muddy the waters in interviews with answers like the ones quoted by others here. My theory is the misspelling of the title is his way of paying tribute to Enzo Castellari's original film, while making his title different. He didn't remake the original, he was inspired by it. The original plot only superficially has a resemblance to the newer film. I believe it also reduced confusion with the original.

To prevent the name being censored in listings

What looks better in listings?

• Inglorious Basterds
• Inglorious B******s

Since social media is pretty endemic these days, this gets the name of the film out there without automatic censor software bastardizing (sorry) the title.

I have no source for this theory, but it seems a pretty Tarantino thing to do.