Why is there are a silent or redundant “W” in words such as wrap, wring, wrong, write, wrist, wreck, wrath, wraith etc?
Because once upon a time they were not silent.
Because those words used to be pronounced with a “vr” or “wr” sound.
Because Samuel Johnson didn’t drop them when he created the Dictionary of the English Language in 1755 which locked down English spelling for the rest of history. Even despite some sounds had been dropped by speakers for almost a century at that point.
The ⟨wr-⟩, ⟨kn-⟩ and ⟨wh-⟩ consonant cluster reductions specifically result in lots of vestigial letters. The ⟨wr-⟩ cluster became ⟨r-⟩ somewhere around the 17th century.
Ok, now tell us why there’s a D in DPRK.
Interesting.
That was true in Proto-Germanic, but if you go yet further back in time (Porto-Indo-European), several of them were again pronounced just “r-“. “Write,” for example, is cousin to “rodent” — scratching.
ETA: Partly ninja’d by pulykamell (not the first time!).
Remember that the spelling, even in Shakespeare has been “fixed” by later writers.
Here is a random selection from the taming of the shrew with the original spelling from several of the original folios as an example. What you read in school doesn’t just lose the long S, the spelling is changed and in some cases the jokes are lost due to both the vowel shift and consonant cluster reductions. While we don’t know for sure knight and wrap would have been fully pronounced at this time.
Argh. “Write” (Germanic) and “rodent” (Italic) both meant “scratching,” but it seems they probably come from different PIE roots. (John McWhorter led me astray on this one - or maybe he’s read something persuasive I haven’t).
So I could once have vritten about how I vrecked my vrist while vrestling? I can hear the difference between “Vr” and “R”, but what about “Wr” and “R”? Would I have weritten about how I werecked my werist while werestling?
No, you would have written about how you wrecked your wrist while wrestling, like you do now. The difference is that in speech you would also have voiced the ‘w’.
Or, to be more accurate, you would probably have voiced a sound which is somewhere the values given to ‘v’ and ‘w’ in most modern variants of English. This sound survived in some variants of English until quite recently; when Dickens has his Cockney-speaking characters say things like “werry well” and “werry sorry” this is the sound he is alluding to, and he evidently expects his readers to consider it distinctively Cockney.
All I know is two wrights don’t make a wrong, they make an airplane.
Afrikaans, like Dutch, has retained the pronounciation. And Afrikaans w sounds like English v.
Noah Webster would like to have a word with you.
The w modifies the pronunciation. I pronounce wrap differently from rap, for instance. I’m not sure how to explain it but the r in the latter is harder and the position of my lower jaw is different.
Surely that’s “wourd”? 
That’s the “except in dialects” in pulykamell’s post. Thing is, “except in dialects” can include a lot of speakers! I recall encountering that differentiation in multiple Jamaican and British speakers (not all Jamaicans, same as not all Brits: dialects don’t follow color blobs in a map).
Do you pronounce the w in wry? When I say the word, it is largely similar to rye, but my lips move differently. Not being a native speaker, I’d like to know how all y’all do it.
I don’t know how “write” was pronounced, but I can see how it could have been pronounced differently from “vrite”. The latter would be a voiced labio-dental fricative. Lower lip against upper teeth and air forced between the teeth and lip. Instead put the two lips nearly together and force air between them and you get a different sound, somewhere between v and w. I believe that that is how the German w is actually pronounced.
I’m surprised it took this many posts in this thread for someone to say this - I also pronounce “wr” words differently than their alleged homophones. The “w” tends to soften the initial sound, as Quartz said - my lips make a rounded shape when beginning these words. It’s almost the same shape as I’d make if whistling.