Oswald the Lucky Rabbit was introduced in 1927 and was designed to be an all-cartoon series to replace Walt Disney's and Ub Iwerks' earlier success, the Alice Cartoons, which featured a live-action girl named Alice (based loosely on Lewis Carroll's classic character) who was caught up in various cartoon adventures. Oswald was a huge success in the silent film era of cartoons and his popularity even rivaled that of Fritz the Cat, but due to a poor business arrangement and a deceptive contract, Disney lost the rights to the character, which then became the sole property of Universal Pictures.
Oswald's look and characteristics would be revamped numerous times after he was taken over by the creative team at Universal. In some ways, Oswald is probably best known as the precursor to Mickey Mouse, as when Disney lost the rights to the rabbit character to Universal, he and Ub Iwerks set about creating a new animal cartoon character to replace him and the result was Mickey Mouse (who many people have pointed out looks rather similar to Oswald only with rounded ears and a short bunny tail).
Oswald is perhaps most famous today amongst film historians and film students who are fascinated by early animation during the silent era and the history of the Walt Disney Company.
Today, the Walt Disney Company once again owns the rights to the Oswald cartoons since they re-acquired them in 2006 when Disney-owned ABC traded sports newscaster Al Michaels to Universal-owned NBC for the rights to the character and the original 26 animated short films. It was jokingly said that it was the first time a network had traded one of their top sportscasters for a cartoon.

Sure, Oswald doesn't get the same kind of press that Mickey does, nor is he as iconic as the famed cartoon mouse, but I seem to be part of the minority who prefers this earlier Walt Disney and Ub Iwerks creation of the silent film era.
One of the things I love is that Oswald's animated shorts are non-stop slapstick action and comedy. Since the characters have no voices, there's a lot of focus on developing expressions and performing physical comedy gags. Plus, let's face it, he's just a cute, mischievous, little character like Charlie Chaplin in cartoon rabbit form.

What's not to love?!