No official Star Wars source has ever answered the question of why Yoda speaks backwards. One possible explanation is that his speech patterns are simply how his species talks. The lack of evidence makes it difficult to prove or disprove this theory. In the entire Expanded Universe, we only see four examples of Yoda's species: Yoda himself; Yaddle, the "female Yoda" who appears in the Prequel Trilogy; Minch, from a short story in Star Wars Tales; and Vandar Tokare, from Knights of the Old Republic.
Yaddle and Minch have speech patterns similar to Yoda, but Vandar Tokare's speech sounds like typical, unaccented Basic. Is the difference merely a separation in time, since Knights of the Old Republic takes place four thousand years before the Prequels?
Another explanation is a difference in language. Yoda's syntax resembles that of a non-native English speaker who imports sentence structures from his native language. This could explain why Vandar Tokare doesn't have the same speech patterns, if he was raised speaking a different language. Still, Yoda is 900 years old -- certainly he's spoken Basic long enough to learn the rules of the language.
In Fate of the Jedi: Backlash by Aaron Allston, Ben Skywalker provides a theory from a different angle: "After nine hundred years, [Yoda] was sick of hearing the same old things the same old way. Use the same old cliché phrases too long and people stop hearing their message." Luke finds this explanation plausible, and it fits best with what we know of Yoda's speech patterns.
Language Log points out several discrepancies in Yoda's backwards speech: while he will often order sentences as Object-Subject-Verb ("Around the survivors a perimeter create"), he also switches entire phrases ("When nine hundred years old you reach, look as good you will not"), splits verbs ("Begun, the Clone War has"), and sometimes even uses a normal word order ("War does not make one great").
This odd mix of syntax offers more support for the idea that Yoda's just doing this intentionally. He wants people to hear his message, as Ben hypothesizes, and uses whatever phrasing will make them listen. On the other hand, this explanation fails to explain why other members of Yoda's species speak backwards as well.
We may never get an official answer for why Yoda talks backwards. George Lucas has purposely shrouded the character in mystery -- his species doesn't even have a name. All we can know for certain is that Yoda's strange speech patterns, no matter why they exist, are a memorable and iconic part of the Star Wars films.