StoneyB, Lass, and Wright have outlined the recent history of initial WR simplification. The ancient history of how they got that way is interesting, too.
I checked the American Heritage Dictionary of Indo-European Roots and found, to my surprise, that all the words beginning with wr- in the American Heritage Dictionary (with etymologies traced to Proto-Indo-European, which includes all the words under discussion here) come from just two PIE roots:
*wer³- Conventional base of various Indo-European roots; 'to turn, bend'.
Derivatives include stalwart, weird, vertebra, wrath, wrong, wrestle, briar, rhapsody, and worm.
*werg- 'to do'. Derivatives include work, urge, energy, allergy, wrought, irk, wright, bulwark, and boulevard.
Note that both of these roots have a vowel between the W and the R. That's not always true in the words they form, however. That's because of the Schwundstufe.
Indo-European, as far as we've been able to figure out, used vowel switching patterns regularly (the phenomenon is called Ablaut, a German term), so that for a given root, it is common to find both "E-Grade" and "O-Grade" words in daughter languages, like Latin pedis vs Greek podos, both meaning 'foot'.
There's a third Grade, however, called "Zero-Grade"; that's where the vowel is neither E nor O but rather absent. I prefer to mangle the original German, and internally parse Schwundstufe as 'disappearing stuff'; sounds both mystical and official. And it's suitably vague about the epistemological status of the "stuff".
And that's what wright and wrought and wrath and wrestle and so on come from. They're Schwundstufen. They come from processes or previous alternants of words with that root where the vowel became superfluous and was dispensed with. These always conform to the pronunciation norms (the phonology) of the people speaking them at the time; when these norms change, as Lass explains in StoneyB's answer, things happen.