When I go to the Korean supermarkets in LA, I usually see half an aisle just dedicated to 고추가루 in all kinds of forms (mild to spicy, fine to coarse grind) and colors.
I don't know that there's any specific pepper than it is all about how sweet and mildly spicy 고추가루 is supposed to be.
You could start from there to make your own by sun drying and crushing whatever peppers are available to you.
If you are looking for a substitute that you can buy at a western store, try crushed red pepper flakes (the kind you see in the shakers at pizza places).
You're going to be adjusting for taste/spiciness anyway, so not much of a dealbreaker.
cooking.stackexchange.com/users/4763/janeylicious
Mc Cormick now makes Korean Red Pepper Flakes for sale at some Costcos (also in smaller containes at the Supermarket).
I bought a large container and I am going back for more.
Great flavor and heat for just about everything.
cooking.stackexchange.com/users/14685/Demerson Carroll
The county I live in produces a lot of chillies called Cheonggyeol (청결).
They also produce gochugaru here.
Here's a link .
After some asking around, I can confirm that these are the peppers they use to make Gochugaru (고추고루).
cooking.stackexchange.com/users/9605/Danger Fourpence
Buy dried chilis and blend them into powder
It sounds like this community doesn't know more about the specific peppers used (and their North American subsitutes) than what @janeylicious has proposed.
Howeover, I propose a different methodology for finding a good fit.
You can buy dried chilis of many varieties from Latino and sometimes American grocery stores: anchos, de arbols.
pasillas, moritas, guajillos, puyas and more.
Turn a chili or mix of chilis into a powder by putting them into your blender or food processor.
Pro-level blenders like Ninjas, Oster Versas and Vitamixes are great for this.
Use the homemade powder as your recipe directs, and compare the taste to how you remember.
You can use a chili guide to inform your adjustments.
Eventually, you should be able to do much better than red pepper flakes for pizza.
cooking.stackexchange.com/users/47791/Merchako
It's really hard to find substitute because the way it is processed is different too.
I'm not sure what the chilies are called but they are quite long and slender.
The Korean ones are bright red and sweeter and the ones in western markets are pretty dark and bitter.
cooking.stackexchange.com/users/6000/Sandra 
If you are unable to locate the real Korean pepper powder, I think you will have to make a blend of your own.
Ancho chilis have a fairly similar flavor, but are not hot enough.
So you would have to mix some amount of a hotter powder into ancho powder, and that could give you what you seek.
Nothing is going to be perfect, but this can get you to a reasonable facsimile.
cooking.stackexchange.com/users/2832/Sean Hart
Yes, you can buy just about anything from Amazon, but sometimes "the hard way
" is more fun, and you get to put that much more love into your K-food.
This is certainly not the authentic Korean method of making gochugaru, but it works for me, and my kimchi turns out great!:
Find a relatively "fresh" bag of dried "Chiles Japones" in the Mexican/Hispanic section of your grocery store; at least 6oz.
(You want them to be slightly pliable; if they are overly dry and brittle, the next step will be frustrating, if not painfully impossible.)
Carefully remove and discard ALL the seeds and stems from the dried chiles; don't worry, it will be plenty spicy (and much tastier) without them...
please, DO NOT scratch your eyes or touch any other sensitive part of your body at this point...
ouch!
Put all the nice red parts in a coffee/spice grinder and process until it looks just right... like flaky dust (dusty flakes?)
... you'll probably never want to use that grinder for coffee beans again, but it's worth the sacrifice.
3.5
No matter how pretty it looks, DON'T sniff it; you'll be sorry
(like I was the first time)!
Now you have something that looks and tastes a whole heck of a lot like Gochugaru...
Proceed to make yourself some Kentucky Kimchi ("Kentuck-chi"?), and let us know how it turns out!
cooking.stackexchange.com/users/47724/Joseph LoGiurato
You can order from Amazon.com if you can not find in market near you.
cooking.stackexchange.com/users/25748/sue
I find Aleppo chilies are quite similar.
They’re also at the same heat level as the Cheonggyeol peppers.
(10,000 scoville).
cooking.stackexchange.com/users/73180/Tyler
I'm trying to make kimchi, but I don't have any chili powder (gochugaru  -고추가루). Does anyone know what type of chili pepper(s) this is made from? I'm trying to find it at a normal western grocery store (Wal-Mart, Kroger, Remke...) I figured if I knew what type of peppers it was made from I could find something equivalent.
What kind of peppers are used in Gochugaru (고추가루)?
cooking.stackexchange.com
<asian-cuisine><chili-peppers><kimchi><korean-cuisine>
cooking.stackexchange.com/questions/14335
cooking.stackexchange.com/users/5617/에이바
You can make a blend of your own if you are unable to locate the real Korean pepper powder. Try using crushed red pepper flakes, especially Korean red pepper flakes. You can use chillies called Cheonggyeol (청결), Ancho chillies or Aleppo chillies, which are quite similar. If they are unavailable in a market near you, you can try buying dried chillies on Amazon and blending them into powder. Try red pepper flakes from Costco or try making your own mix from various chilis.
Try red pepper flakes from Costco. Chillies called gochugaru, anchu, aleppo or cheonggyeol have quite similar flavours. Make your own mix from chilis or order from Amazon.