John Wick's backstory has never been explicitly explained in the films or accompanying comic series. Though the third film or prequel TV series may give us more concrete evidence, we've been given enough puzzle pieces to confidently say he served in the U.S. Marine Corps.
Given his extreme handiwork with firearms, hand-to-hand combat proficiency, cold demeanor, proper posture, and dispensation of absolute wrath towards anyone who harms the things he loves, it's not too much of a stretch to say that he once was a Marine. No single point is definitive proof but it's fun to speculate.
Chad Stahelski, the director of the franchise, was asked by Collider in a 2017 interview about John Wick's backstory. He said that the series isn't about overloading the audience with dry exposition, but rather shows the audience little things. Stahelski said,
"We're giving you the pieces and I think it's always good… Hopefully in five years, you and your buddies will talk about how 'he's this or he's that.' We'll give you a couple more pieces and let you stitch it together."
It's the minor details that give one troop away to another in the civilian world and, right about now, our veteran radars are going off.
1. The tattoo
The most obvious indicators of military service are his tattoos. While most point to his faith, the Latin phrase on his shoulders is a dead giveaway.
John's tattoo reads, "Fortis Fortuna Adiuvat," or "fortune favors the brave" in Latin. This is also a lose translation of the motto of the 2nd Battalion, 3rd Marines — although their spelling is "Fortes Fortuna Juvat." This is common enough that it's not conclusive evidence alone, but it's definitely a starting point.
2. His watch
Another blink-and-you'll-miss-it detail almost exclusive to the military community is the style of his watch and how he wears it. It's got a leather band and he wears it on the inside of the wrist of his non-dominant hand.
War fighters chose not to wear anything reflective as to not give away their position and, by wearing it on the inside of the wrist, it's easy to keep from breaking. This, however, would also be common among professional hitmen.
3. His relationship with Marcus
It is strongly hinted at that Marcus was a mentor to John in the past — he taught him everything he knows about firearms and helped bring him into the world of underground wetwork. Given that their age difference isn't too extreme, it would make sense that Marcus was once his NCO. This would also explain why after John walked out on the life of crime, Marcus was able to stay — because he was there before they both became hitmen.
This theory is also backed up by the film's color palette. Everything in the film is cold or red — except things dear to John. Take, for example, his wife's gold bracelet, his dog's tag, and Marcus' clothing and home decor. There's definitely a closeness here; it's up to us to speculate why.
4. Apperance in 'Payday 2'
This one should be taken with a massive grain of salt because it involves evidence from Payday 2, not the John Wick franchise. He was a community unlock in 2014 and had more DLC added during the second film's theatrical release.
The game doesn't hold back on explicitly saying that John was a Marine and was brought into the Payday Gang by a series regular, Chains, who is very open about his prior military service.