The proper phrase, of course, is to "wreak havoc," but after seeing the homonym used in its place yesterday, I decided to look up the phrase.
A Google search is a decidedly blunt instrument to investigate frequency of usage*, but a quick check yesterday yielded 600,000 hits for "reek havoc" vs 6,000,000 for "wreak havoc." So it's not a grossly misused term.
But "wreak" is in itself an interesting word. Here's an abbreviated summary from Wiktionary:
Etymology: Old English wrecan... from Proto-Indo-European *wreg- (“work, do”). Cognate with German rächen, Swedish vräka... and distantly cognate to English wreck.
wreak... simple past wreaked, wrought (erroneously), or rarely wroke
Definition: To cause, inflict or let out, especially if causing harm or injury... (archaic) To inflict or take vengeance on.
So what can you wreak? Again, just from Google - havoc, damage, destruction, revenge, devastation, mayhem, pain, terror, carnage, toll, fury, Hell, chaos, and genocide.
*any suggestions for a better tool to use for this?