While I won't say the criteria is hard fast, the basis for making it here on this thread: Recognized recipe with many replies, stars, and testimonials. This is for the tried and true. This is what you point someone to who is looking for some new ideas or trying to branch out.
This is not to say there are not other FANTASTIC recipes out there. This is just a starting point for the newer'ish brewer or someone looking to break into a new-for-them style of beer.
I have personally brewed each of these recipes below and will and do gladly brew them over and over again. Each of the titles is a clickable link to the recipe. Hopefully someone finds this helpful!
Apfelwein: This is a great "1st brew" and I am going to go out on a limb here and say this is probably the most home brewed recipe of all time. It takes very little equipment and effort. Your friends will be amazed you made it.
Skeeter Pee: Another recipe with literally millions of brews. Very little experience needed and a very adaptable recipe. Some people have success with no slurry, some always do a slurry. The typical way to do a batch of Skeeter Pee is to brew a batch of Apfelwein then use the slurry for your Skeeter Pee. I have used the same slurry 3 times (Apfelwein, Skeeter Pee, Skeeter Pee) with great success.
Rice Wine: Grocerey store friendly. You can have this brewing within 45 minutes if you have an Asian market anywhere in your hometown. While I wouldn't say the outcome is universally loved, it is unique, different, and packs a punch!
Cream of Three Crops Cream Ale: Your intro to Biermuncher, who will be your idol for the first 2 years of brewing. A classic standby that is a great easy intro to All Grain. All BMC'ers you know will be shocked you made it and will make excuses to visit and drain your supply.
Vanilla Cream Ale: I have personally taken Best of Show in a homebrew contest with small adaptions to this recipe. This is another recipe for the masses that love BMCs. A real winner! Smooth, creamy, vanilla-y, pure goodness!
Berliner Weisse: This should be your first Sour. It is all extract and can be made in 2 hours end to end easy. I don't even bother breaking out the "real brewing gear" when I make this. Largest pot you have, boil the extracts and the hops for 15 mins, cool it down, fill up the carboy with purified water and pitch a dry packet of US-05 and this thing is off and running. I have brewed this and had it kegged and drinkable in 1 week. No joke, 1 week. I think its best on the 3 week timeline, but certainly drinkable after 7 days if kegged. The sour is added lactose (2-3 oz depending on how sour you want it). The recognized syrup to add is Raspberry. The other two common flavors are Lemon and Woodruff. Red, Yellow, Green aka the Stoplight.
Lemon Lime Hefewizen What's not love about a Lemon-Lime Hefewizen?? The perfect summer beer!
Cottage House Saison: As this beer style grows in favor, you will want to try it for yourself. I found this to be a fun brew day and the wait for the final product to be well worth it!
Augustiner Lagerbier Hell: An AG light lager that is a great first lager and another one that people will be amazed that "You made this?"!
Common Room Extra Special Bitter (ESB): A great intro to hoppy beers but not an over the top beer. You will find it extra pleasing if you are a fan of English hops.
BierMuncher's OktoberFAST Ale (AG): A great beer to brew and time to be ready for Oktoberfest. When you think of a great Oktoberfest beer, this is it.
Raging Red Irish Red ale: At some point in your brewing career, you will want to brew an Irish Red. This is a great starting point!
Centennial Blonde: I swear I am not in love with Biermuncher, he just has a ton of truly great recipes. This is that classic "Blonde" recipe.
Yooper's Dogfish Head 60 Minute Clone: Dogfish Head's 60 is a standby IPA available nearly everywhere. Now you can brew something that will also be universally loved by the hop heads in your crew.
Black Pearl Porter: Another Biermuncher masterpiece. If you like a sweet English style porter, this recipe is the best a great intro to homebrewing something with a bit of meat to it.
Deception Cream Stout: I am not a huge Stout fan, but I liked this one better than anything I have bought off the shelf.
Pirate Ale: j1laskey deserves an award for this one. THE sleeper recipe on HomeBrewtalk IMO. Brew this up and you will be blown away if you like big strong style ales. I refuse to not have this either on tap or in the pipeline at any point in time. Just an amazing beer that I can't say enough about.
Water into Barleywine: Another AG Strong Ale / Barley Wine, but definitely worth brewing! The one batch I made I drank before I think it was fully conditioned, it was that good!