Too many writers suffer at the hands of these two words.
Rack, as a verb, generally means to torture (rack my brains). As a noun, it can mean a variety of things, but the forms most often misspelled are those referring to an instrument of torture (The inquisitor planned to stretch his limbs on the rack.) or to be in a state of deep anguish (racked with sorrow). Rack as a noun also can refer to a frame, this its use as a verb in rack up points or rack billiard balls.
Wreak, as a verb, means to wreck (to wreak havoc). As a noun, it means ruin or destruction (Cleveland has been going to wrack for decades.).
The easy way to remember the difference is rack = torture while wrack, with an extra letter, goes the extra step of actually destroying something.