צבא הגנה לישראל Tzva Haganah LeYisra'el,note Literally, "The Defense Army for Israel" known in English as the Israel Defense Forces, or Tzahal (from its Hebrew acronym) to its friends. Formed in 1948 from the various La Résistance factions of the time, involved in at least one war per decade, usually against numerically superior Arab forces, all won, except for the 2006 invasion of Lebanon, which is up for debate (depending on whether you consider victory to be decided by kill ratio or objectives achieved). In terms of flying skills (as measured in tactical exercises vs American and NATO forces) the IDF has some of the best pilots in the world. This is also evidenced by their very good record against Arab aircraft, even if said aircraft are downgraded export versions of Soviet stuff—though for most of the wars, Israel's aircraft was even worse. (Israel is partly able to make up for it with superior mobilization, this can be considered a real life example of Conservation of Ninjutsu). As a result, if you're looking for an Ace Pilot post WWII, Israel (or Pakistan) should be the first place you check.
The State of Israel uses universal conscription of both sexes note For Jews who are not Haredim aka Ultra-Orthodox, many of whom are excused from service in order to study at religious schools (there are some Ultra-Orthodox who do serve, and at least one military base designed specifically for their needs). This exemption is very controversial amongst secular Israelis, who feel the Haredim get a free pass, and there have been efforts to lift it (in addition to being considered unfair, it is also hoped that serving in the army would allow Haredi youth to learn practical skills and become more engaged in Israeli society as a whole. It is suspected that part of the resistance amongst the Haredi community is for exactly this reason). Israeli Druze also have to serve, as do male Circassians (a mostly Muslim Caucasian minority that moved to Israel after their homeland was invaded by Russia in the 19th century). Non-Druze Arabs are excused, although some do volunteer (largely Bedouins and Palestinian Christians) This has resulted in the IDF gaining a reputation for hot female soldiers.
Israel's principal military supplier until the early 1960s was France. The United States became Israel's major supplier after the Six Day War and remains so until the present day. However, over the decades Israel has developed its own defense industry, developing, among others, a number of local aircraft, an indigenously developed series of main battle tanks and APCs, several types of missile boats, various firearms, rocket and missile systems, combat related robots, electronic warfare systems and a wide range of UAVs. Despite this, what most people would probably say when asked what weapon was made in Israel, would probably be "the Uzi".
Israel was also the first export customer for the F-15 Eagle and first to use it, as well as the F-16 Fighting Falcon, in combat. The Israeli air force is still responsible for over half the air to air kills for both fighters to this day.
Due to Israel's universal conscription, it is often assumed that all Israeli adults have military training, and are therefore combat capable. This is not entirely true, as Arabs (but not Druze or Circassians) are exempt from conscription, and previously so were ultra-Orthodox Jews (their exemption is in the process of being phased out due to Israeli courts ruling it unconstitutional), and usually do not serve. Also a non-negligible percentage of the population that does need to serve avoids it anyway. So not all Israelis have military training... just most of them. It's also important to note that most of the IDF's personnel are non-combat soldiers that have only a very basic combat training.
Officially Israel neither confirms nor denies possessing nuclear weapons. Even though everyone is pretty sure they possess them.
Related to this is the Israeli intelligence service. The Mossad (the Israeli counterpart to the CIA) is infamous for carrying out assassinations, as well as being very good at their job in general.
See also: Arab-Israeli Conflict, The Samson Option.
Break Out the Museum Piece: Early on, Israel had almost no weapons to speak of, and were willing to take whatever they could get. One example is their use of WWII era M4 Sherman tanks throughout the Cold War. Despite being obsolete, the Israelis aggressively upgraded the Shermans to the point where they could engage (and even curbstomp!) Soviet Cold War era tanks.
Catch Phrase: Several, some officially supported by IDF culture and some unofficial truisms emergent from the lower ranks:
"These orders were written in blood." (tagline of many a list of safety guidelines)
"Results - not excuses."
"Difficult in training - easy in battle."
"That's all we have, that's what we'll win with."
"Painted is new; wet is clean; piled-up is neat; bureks are festive." (ironic paraphrase of the famous edict from 1984; the closest analogue in English is probably "To Seem, Rather Than To Be". Lampoons the dogmatic culture of bureaucratic appearances, and concurrent lack of focus on substance to go with it, endemic to the IDF when it's dealing with matters not immediately relevant to its ability to shoot at enemies.)
"If it moves, salute it. If it doesn't move, pick it up. If you can't pick it up, paint it white."
"I was born crying; When I was drafted, I realized why."
"The man in the tank will win" (armored corps)
"When you see a sniper, don't run - you'll die tired".
"If I don't get to fly, NO ONE gets to fly." (unofficial motto of the anti-aircraft unit, allegedly full of would-be pilots who dropped out)
Cool Plane: One of the best airforces in the world. And it's not just because they have cool planes. Check out the story of ZivNedivi.
Conscription: This allows Israel to punch above its weight in numbers. However keeping a lot of people under arms permanently can hurt the economy.
The conscription is actually believed to help the Israeli economy quite a bit. Its mostly a matter of mental state—there is no shortage of ex-officers with leadership experience, and the military encouraged attitude of taking the initiative. Doing the likes of say, forming a business plan, doesn't seem all that daunting a task for someone who's trained to plan for and keep his head in a life and death situation as part of his job description.
The keywords here are "believed" and "seem", as many Israelis whose bosses are former army officers, will testify. Military officers usually need to retrain extensively to function as civilian managers — probably something to do with employees needing to be asked instead of told.
Here's four. The first: during the Six Day War, the Israelis launched a sneak attack which destroyed almost the entire Egyptian Air Force while it was still on the ground. On the first day Israel destroyed the Egyptian airforce. On the next five they kicked ass with full air support. On the seventh day they rested.
The second: Rallying from near-complete military deactivation on the holiest day of the year to repel an invasion during the Yom Kippur War. The fact that Jews are not supposed to use the telephone or drive on such holidays meant clear communication lines to alert the troops and empty roads for them to race to their posts really helped move things along.
The third: The Raid on Entebbe. If you've ever seen the movie with Charles Bronson, you might think it's over-dramatic. It's not: the raid was that insanely awesome.
The fourth: in 1981, the Israeli intelligence heard that Saddam Hussein was developing a nuclear program. So they sent a squadron of planes to fly over to Iraq - over 600 miles away - and blow it up. And it worked - the nuclear program was delayed by at least 20 years, and when the American troops came to finish the job in Desert Storm, they found out that "the Israelis did most of our work for us".
Better make that five, the very first war the Israelis fought was the 1948 war with the Arabs, and that was the same day it was declared a state. The Israelis fought and repulsed all 10 Arab States that attacked it, marking the beginning of this trope.
Shooting down 80-90 MiG's and destroying 30 SAM batteries without a single loss on the first day of the 1982 war has to count.
YMMV on this, as some Israelis are upset that we have the most depressing national anthem in the world. Where most nations have something uplifting and patriotic, Hatikvah is a big Tear Jerker with a Bittersweet Ending.
Funny, that was what I liked about it. It felt like an anti-jingoistic patriotism in which people could love their country while not forgetting that War Is Hell.
Death from Above: The Israeli Air Force famously used air power as a decisive force during the opening days of the 1967 war. These air strikes are widely agreed to have broken the back of the Arab armies by denying it precious air superiority. They promptly proved this was not a fluke when, on the first day of the 1982 Lebanon War, the Air Force took on 100 Syrian MiG's and 30 SAM batteries, shot down at least 80-90 and destroyed the SAM's...without a single loss.
Eagle Squadron: The Jewish Brigade in World War II serving in the British Army (this only partially counts as Britain was their Feudal Overlord at the time. But it was recruited in that spirit.). Also a number of foreigners during the '48 war.
Elite Army: They certainly seem like one, given the incredibly lopsided casualty ratios of the conflicts they get involved in.
Enemy Mine: They had a briefly cooperated with Iran during the Iran Iraq War, providing military advisers, money, and weapons, as well as bombing an Iraqi nuclear reactor during Operation Opera, mostly because they really hated Saddam Hussein. This was in contrast to their ally the United States, who regarded Iran as the bigger threat.
Actually, they created bullets in secret and pretending that they were lipstick tubes. The real thing wouldn't make a very good bullet. They also hid weapons inside of milk cans and explosives in gas tanks of trucks to hide them from the Brits.
Initiation Ceremony: For most units, basic training concludes with a long march to a historically or otherwise significant site (depending on the unit, usually Masada or the Western Wall) to be sworn into the IDF and receive their corps berets.
Irony: Due to their almost single-minded emphasis on individual initiative, rapid victories, and maneuver warfare, the IDF best resembles the operational doctrine of the Wehrmacht.
For an additional layer, IDF infantry were originally armed largely with surplus weapons seized from Nazi stockpiles. They acquired weapons from absolutely anywhere they could find them, and there was was no larger source of weapons in the world than the now-disbanded Wehrmacht's stockpiles. Some even still had swastika designs engraved or enamelled on (the first thing IDF men did was scratch them out with rocks)
The first ever fighter aircraft acquired by Israel? The Messerschmitt Bf109.
Who provided Israel with heavy water to boost their nuclear power - and eventually making them capable of making their own bombs? Norway, of all nations...
Mildly Military: Ironically for a force so reputed, the IDF has historically been lax on discipline, even touting it as something that lesser armies need. This has, on occasion, bitten the IDF in the ass.
In particular, the Golani Brigade is known for both its fighting prowess and its discipline problems.
Open Secret: Israel's nukes. They haven't officially revealed them yet, but when then-Prime Minister Ehud Olmert accidentally (or perhaps accidentally on purpose) said (or at least implied with barely less subtlety than actually setting off one of the nukes) that Israel had nukes in a speech in 2006, the world barely noticed. Of course, there isn't much reason to keep a nuclear arsenal secret—the main point of having it is intimidating the other side not to attack, something a secret doomsday device isn't so good at. The reason for Israel going this route is strategic. Israel's potential regional enemies (e.g. Iran, Iraq, Egyptnote We should note here that Egypt was never particularly serious about developing a bomb, whatever Tom Lehrer might say. And that whole "regime change" makes Iraq highly unlikely to try again any time soon.) know it has nukes, and are thus deterred from military action that would threaten Israel's existence. They can't acquire their own nukes because they're parties to the Nuclear Non-Proliferation Treaty (NPT), which forbids owning any (except for the US, Soviet Union/Russia, China, the UK and France) and subjects them to IAEA inspections. And they can't withdraw from the NPT without an "imminent threat" to their security (such as a nearby rival having nukes already), which officially doesn't exist because Israel officially refuses to confirm anything.note In theory, at least. In practice, any nation can unilaterally withdraw from a treaty at any time. But doing so with the NPT would be such a diplomatic nightmare (and very likely a trigger to war) that not even Iran in its increasingly defiant nationalism has shown any willingness to risk it. In other words, it's an endless cycle of I Know You Know I Know and Willful Blindness on both sides. This serves the interests of both Arabs and Israelis: the Israelis get their security and their neighbors get a good reason not to fight Israel and also keep the Middle East a nominal nuclear-weapons-free zone; the ambiguity also spares the regional powers the expense of developing their own weapons programs. (Israel's interest, by the way, does not include the fear of IAEA inspections, as many Israelis claim; Israel is not a party to the NPT and unlikely to become one in the foreseeable future, so it's not subject to inspections, and declaring its stockpile would have no effect on that—any Israeli politician mentioning inspections is just trying to scare you.)
Pint-Sized Powerhouse: Israel has a smaller territory and population then several states in the area, and it is probably the most feared.
In this case, "smaller territory" works out to "about 200 miles long, and about one third of that at its widest."
Proud Warrior Race: This actually goes all the way back to the ancient Hebrews, who were renowned as warriors.
Refuge in Audacity: The IDF has, I shit you not, designed a gun which consists of a rifle with a stuffed cat on the end of it. The entire purpose is to cause the enemy to hesitate in firing at a "cat", thus giving the Israeli time to get a few shots of their own in.
Operation Noa. Israel paid France to build a set of missile boats, and then France imposed an arms embargo and refused to deliver the goods. So over the course of several weeks, all the people necessary to man the boats went to Europe in ones and twos, making their way to Cherbourg while in the guise of tourists. They even bought the supplies necessary for eight days of sea travel at local grocery stores. Then, on Christmas Eve, they simply walked in and stole the boats.
The Scrounger: On one notable occasion, one Haganah agent was negotiating with a Czech Arms Dealer. To get the money needed he had to collect it from private contributions, doing things like walking into the local Jewish quarter and drumming up money.
The attack on the fortified Old City of Jerusalem during the Six-Day War.
Took a Level in Badass: Twice. Once when the Haganah learned to hunt down Arab guerrillas during the Arab revolt against the British (One British writer said: "They discovered that they were soldiers."). And in the Six-Day War when they surprised everyone by how much they had changed from the Militia they once were.
Training the Peaceful Villagers: The British Officer Orde Wingate did this for the Haganah militia. Including a 20-year-old Ruth Westheimer, trained as a sniper and wounded in the '48 war. "Pint-Sized Powerhouse", indeed.
Trigger Happy: Understandably so - they are surrounded on all sides by nations that are not only hostile but want to end Israel's existence. Then there are the Palestinian terrorists, who operate from urban areas.
Up Through the Ranks: The majority of the Israeli officer corps qualifies, since they have no officer candidate schools.
Worthy Opponent: The Jordanian Arab Legion, the only Arab military that consistently held its own against the IDF. The West Bank would probably still be Jordanian if the IAF hadn't destroyed almost the entire Royal Jordanian Air Force in the first day of the Six-Day War, granting the IDF the advantage of air support.
Mirage by James Follett, a spy thriller detailing exactly * how* the Israelis managed to get the Mirage aircraft from the French.
Spooks Accidentally kills about 70 kids in a Gaza school
Eagle in the Sky- A Wilbur Smith novel that features a South African join the IDF, then get thrown out after chasing Syrian fighters into Syria, losing his wingman and getting disfigured in the process.
Independence Day - In an interesting example of... optimism... Israeli and Syrian pilots hide aircraft in the Golan heights and launch a combined attack on the alien fleet after the American example.
The Zombie Survival Guide: An Israeli paratrooper platoon stops a zombie outbreak in an Egyptian village in the 70's. Trading zombies as biological weapons leads to the Egypt-Israel detente.
World War Z, from the same Verse; the IDF ends up enforcing a voluntary quarantine of the country after the Outbreaks begin, and has to fight a civil war with the ultra-orthodox as a result of this and other security and practical measures.
Y: The Last Man: being the only people in the region to employ female soldiers puts Israel in a strong position when all the men die. IDF leader Alter becomes a major antagonist in the series.
Tom Clancy's Endwar: Israel is officially neutral in World War III, but very, very quietly aids and supports the European Federation.
Tom Clancy's The Sum of All Fears opens during the Yom Kippur War, where a nuclear armed IDF aircraft is lost in action, providing the MacGuffin for the plot. In modern times, as part of the peace agreement the US Army's 11th Cavalry is stationed in Israel, and as part of their training plays wargames against the IDF.
While not precisely a member of the IDF, Earth Force Colonel Ari Ben-Zayn (a one-shot character) from Babylon 5 plays on all the tropes about the suspicion and toughness of Israeli soldiers—and has a massive scar to show for it. Ben-Zayn loosely translates to "Son of a Gun", and is also slang for dick, so that makes it a Bilingual Bonus with several layers.
You Don't Mess With The Zohan parodies this trope to no end with Zohan (Not an Israeli name) Dvir (An Israeli name), a supersoldier who can do push ups with no hands, kick two people at the same time, leap over walls, run on ceilings, and feel no pain from a piranha in the swim-suit. He has a Palestinian equivalent called the Fantom, too.
The "all Israelis have military training" is invoked in Vortex by Larry Bond and Patrick Larkin. In order to take out South Africa's nuclear arsenal, the US military enlists the aid of an Israeli professor who helped the South Africans develop said arsenal. The original plan called for the professor to train the American commandos in disarming nuclear warheads. When developments force the op to launch ahead of schedule, the American commander decides to take advantage of the professor's military training (he was an infantryman) and have him come along. The thinking is that even if he's just an infantryman, he'll be able to handle himself on a battlefield.
Ziva David from NCIS was a Mossad kidon operative.
In How to Ruin series by Simone Elkeles, Amy spends a summer in Israel and meets a guy named Avi, who is in the military there. In the third book in the series, she follows him back to Israel and signs up for military training.
Mentioned briefly in Black Lagoon by Ibraha, who calls them "Those monsters from Jerusalem!". Unfortunately, they're never actually seen.