For spies, combat is an absolute last resort. They’ll use it because they have to. When they do get into combat, what they’ll do will be heavily dictated by who they’re masquerading as.
If they need to eliminate someone to avoid blowing their cover, they’re going to need to take them down as hard and fast as possible. Preferably in a way that doesn’t point back at them. Sometimes this means killing their opponent, but as Westen points out throughout the series, leaving a dead body behind can actually draw more attention in the long run.
Like most genres, spy fiction ends up on a spectrum between formalism and realism. The issue is, at the extremes, they’re almost different genres, so I’m basically going to have to write two separate recommendation lists.
The formalistic genre is your superspies. This ranges from espionage themed action to comic book level insanity. Your spies are a different flavor of superhero. As a tonal element, formalistic spies actually work better when placed against supervillains, because you get a nice parity between them.
The realistic genre is the brutally bleak tradecraft. These are settings where spies will die if they get into actual fights with trained opponents, and saving the day often means outmaneuvering your opponents without resorting to overt action. At its extreme, the realistic genre can actually get bleaker than espionage in the real world, and that’s saying quite a bit.
The best material in the genre finds a mix between these two points, and stays there. So, you’re going to get two separate recommendation lists, just remember to take elements from both.
Burn Notice’s is a bit schizophrenic. The narrator isn’t just a completely different character from Michael Westen, he’s actually at a different point on the spectrum. The show itself is fairly formalistic, while the narrator is talking about concerns and behavior from a realistic perspective. It’s part of why the show worked so well, but when you’re drawing from it, remember to keep those elements separate.
If you’re wanting to go more in the superspy direction, James Bond is the gold standard. License to Kill and Casino Royale are probably the most realistic (which isn’t saying much). If this is a good thing or not is a matter of taste.
The Bourne Identity (the first film only) is another solid formalistic example. (The second and third film have better fight choreography, but they suffer from a terminal case of shaky cam; which requires you already have a solid grasp of hand to hand to really follow.) The only part of Legacy I’ve seen was Jeremy Renner’s fantastic hand to hand work. It’s more cop than spy, but if you have the time, it could be worth looking at.
The novel is actually much closer to an American James Bond, with the serial numbers filed off. You can pick up some basic tradecraft from it, particularly Bourne’s thought process about blending into his environment can be very useful, and it’s something the film does skim completely over.
Salt is solidly in the superspy genre, the sleeper agents demonstrate supernatural resilience to damage, and the entire premise is a little crazy. But, if your spies aren’t really human, you could probably get some ideas from this.
Red is basically in the same vein, fun, but equally ludicrous. Again, if your spies have actual superpowers, go ahead and watch it. Karl Urban’s character might be worth looking at even if you are pushing for a more realistic bent.
Chuck wore thin for me. There’s stuff to like, so, it might be worth your time if you want to mess around with superspies interacting with the normal world.
The original Get Smart TV series is freakin’ brilliant. It’s a parody of the superspy genre that was partially helmed by Mel Brooks. Obviously, it’s not even remotely serious, but if you’re wanting to mock that genre it’s a must see.
If you’re wanting to run harder into the realistic genre, then you’re going to be looking at a much bleaker recommendation list. I’d start with The Human Factor by “Ishmael Jones”. This an ex-CIA case officer’s memoires, it’s easily available and deals with the current state of the American Intelligence community.
Blowback by Chalmers Johnson isn’t actually about spies per say, but it is about the political consequences of espionage (and foreign policy in general). This might not be something you want to delve into, but I’ll leave it on the list.
With the non-fiction reading out of the way, John Le Carre’s Tinker, Tailor, Soldier, Spy is a classic in the genre with good reason. The novel’s been adapted twice, with Alec Guinness and Gary Oldman playing George Smiley. I haven’t seen either, but the novel is a good primer for writing spies.
The Fourth Protocol follows a retiring spy who’s investigating a Soviet plan to detonate a nuclear weapon on an American air base. Bonus points, in that the Russian agent is played by Pierce Brosnan. If you want to see how a realistic spy fights, then he’s probably the single best example. That said, it’s been about ten years since I saw this, so I could have accidentally slipped on rose colored glasses. I haven’t read the novel it’s based on.
Although somewhat dated, The Sandbaggers was a British TV series in the late 70s. Though the answer it gives on how their spies fight is “as little as possible.” Historically the show is actually based on how the CIA would task agents, rather than MI6.
Greg Rucka’s Queen and Country is a modern update of The Sandbaggers in comic form. I wouldn’t recommend it if you’ve already seen Sandbaggers, but if you don’t have access to the show, then this is much easier, and cheaper to find.
Ronin is a mix of formalism and realism. It’s still an action film, but the tradecraft the ex-spies use is remarkably solid. Given that you’ve started with Burn Notice, you should have a pretty good frame of reference to understand why they’re doing what they’re doing. Also, I’ll say it again, this is also one of the best films you can watch for car chases, almost every shot in the film was done with stunt drivers on actual streets, and it shows. If you want to get an idea of what a trained operative could actually do with a car, this isn’t completely off base.
Spy Game by the late Tony Scott is a rather hectic mix of realistic elements. I’m more comfortable dropping it here because of how heavily cut together it is, and elements of the film’s plot. This is a very dense primer on tradecraft.
The other mix of realism and formalism is the Mission: Impossible TV series. Not to be confused with the film franchise, the TV series focused on characters actually being spies, infiltrating and manipulating organizations or individuals to achieve their goals. There’s a heavy focus on supplementing their operations with gadgets, but it’s one of the forerunners of the modern genre divide.
AEG’s Spycraft RPG was written so it could be played as either a realistic or cinematic (formalistic) game. It has a lot of resources for both superspies and real operatives. In a rare moment, the character creation system is also useful, as it illustrates the different specialties that are intrinsic to espionage.
Spycraft’s World on Fire supplement is insanely useful, it’s also incredibly hard to find. It was about blending one of the Spycraft settings with the real world, and it has an absolutely staggering amount of information on actual espionage in the 20th century. Unfortunately, a lot of it is mixed in with World on Fire’s six fictional factions. So, it’s useful, but tread carefully.
If you’re wanting to do a spy story set in a science fiction setting, I’d take a look at The First Line from Last Unicorn Game’s now defunct Star Trek RPG. Be ready to parse the Trek out of it, if your setting isn’t similar, but it does offer some fantastic thoughts on espionage and counterintelligence in a spacefaring civilization.
Finally, the line from Burn Notice, that “Spies are just criminals with a government paycheck” is entirely on point. You’re probably tired of me recommending Heat every other post… So I’ll recommend Payback instead. The lead character is a con artist, not a spy, but the general “messing with people” approach is very spy like. (If you’re digging this up, make sure you grab the director’s cut, it’s actually a different, more consistent, film.)