Ray Kurzweil, one of the fathers of speech recognition, talks in his book How to Create a Mind about his use of "Hidden Markov Models" as a breakthrough in speech recognition work. I believe Kurzweil used his HMM's to recognize the flow of sounds and speech patterns as words, so it's not exactly the same as what Swiftkey does with word prediction, but it's safe to safe Markov chains have an important place in language modeling.
Hidden Markov Models are also an important tool in computational biology - we use them to represent and search for motifs in sequences, such as DNA binding sites, protein domains with a particular function, etc.
Hidden Markov Models: http://en.wikipedia.org/wiki/Hidden_Markov_model
Kurzweil's Book (He goes into more detail on speech recognition as well as a slew of other topics): http://www.howtocreateamind.com/