"Old English" was spoken before 1150 C.E.
"Middle English" went on to about 1500 C.E.
Shakespeare actually wrote in Modern English, with some holdovers from
Middle English (check out "A Midsummer Night's Dream, Act II, scene 1,
"Swifter than the moone(umlaut)s sphere")
There are several excellent Old English sites out there, with RealAudio
readings from Old English literature such as Beowulf.