D0G, for basically being Alyxs big badass robot companion. Valve responded to his popularity by giving him a major role in the intro of Episode One.
The G-Man himself is quite popular due to the whole mystery surrounding his motivations. People also get laughs out of him through Garry's Mod.
The All-Knowing Vortigaunt from Half-Life 2: Episode 2, simply because people love speculating about what hes telling you.
Adrian Shephard from Opposing Force. Valve themselves have taken note of his enduring popularity and have not ruled out having him make a return at some point.
Genius Bonus: The series is full of references to scientific concepts (starting with the game titles), particularly quantum mechanics and cosmology. This game is where most people first heard about The Challenger Deep, Dark Energy, Singularities or The Calabi-Yau Model.
The teleportation theme seems to be a bit better researched than in most games, as well. It appears to be based on a wormhole principle, which, naturally, requires that Dark Energy everyone talks about.
The headcrabs. Especially the poison ones, which are specifically designed to screw with your ability to deal with other enemies.
Manhacks apply, as well. Those buggers just swarm all over you. Plus they fly! Once you have the Gravity Gun, though, they lose a lot of their annoyance to the "grab and punt" kill method.
The Antlions, who often push you onto sand, causing more of them to come!
Doubles as Fridge Brilliance. Think about bees. A single antlion spotting a threat attempts to force said threat to cause more to come to its aid in case it is more than it can handle on its own.
Hilarious in Hindsight: Half-Life and Lost were made by fans of each other and have referenced each other. Then, in 2017, Marc Laidlaw's plot outline of Episode 3 reveals that the plot had involved the ship the Borealis constantly traveling through time and the only way to find it is to predict where it's going to be, the exact same method given by Lost on how to find the Island that was that show's focus.
Magnificent Bastard: The G-Man is an enigmatic bureaucrat who uses his supernatural abilities to carry out the whims of his "employers". Always watching from afar, the G-Man monitors people who exhibit great survival instincts to employ them under his cause. Responsible for bringing the crystal sample that caused the Black Mesa Incident, the G-Man went against the orders of his superiors to rescue Alyx Vance and Adrian Shephard for his own purposes. The G-Man would rearm a nuclear warhead to destroy the entire facility to cover-up his tracks. When Gordon Freeman killed the Nihilanth, the G-Man recruited him as Xen was now under the control of his employers. Twenty years later, he sent Gordon to City 17 to help overthrow the rule of the Combine. Although he was held back by the powers of the Vortigaunts, the G-Man waited until they were distracted to order Alyx to warn her father about the Borealis. With motives known only to himself, the G-Man removes any sense of choice from the people he manipulates.
Memetic Molester: Many fans like to interpret the G-Man as this, likely because of his bizarre speaking patterns and personality.
Memetic Mutation: What happened when someone noticed that one of the scientists working on the Large Hadron Collider bore a resemblance to Gordon Freeman. The Internet ran with it and went so far as to send a care package of items Gordon would need to save us all once the activation of the collider opened a portal to Xen. The G-Man was spotted too, so you know we're all dead.
Wait a minute, TV Tropes, in total, has eight letters. Two on TV and six on Tropes. Six divided by two is three. HALF-LIFE 3 CONFIRMED! Explanation Thanks to the Development Hell that Half-Life 3 is currently in, many people have gone and went to crazy lengths to "confirm" Half-Life 3 is coming out. Became somewhat Hilarious in Hindsight with the release of Half-Life: Alyx and Valve's acknowledgement that said game would not be their final entry in the Half Life franchise, all but confirming that Half-Life 3 is back in development.
The G-Man's briefcase has never been seen open, and as such fans speculated on what he could be holding in it, including the ever elusive Half-Life 3. Come Alyx, and the G-man allows you to catch and open his briefcase to perform a Cosmic Retcon on Episode Two, and set up the events for the now confirmed Half-Life 3, making the joke true to an extent.
Scientist lines and screams from the first game have become popular as of late. With STAHP and AUGH being amonth the most beloved.
More Popular Spin-Off: Counter-Strike and Team Fortress Classic. Originally, they were simply Gaiden Game multiplayer add-ons to Half-Life, being sold at retail mostly in bundles with the Half-Life games, sharing the bulk of their assets with it, and implicitly being set in its universe by the presence of things like Black Mesa logos in the retail maps. For a while, the only way to even get Counter-Strike: Source was to buy a copy of Half-Life 2. However, the massive success of these games' sequels, Counter-Strike: Global Offensive and Team Fortress 2 has arguably made those series more famous and successful than the one that they spawned from. To wit, Team Fortress 2 was at one time the most popular PC shooter period, while CSGO sold 25 million copies prior to going free-to-play, which is more than Half-Life, Half-Life 2, or The Orange Box... combined.
Paranoia Fuel: Headcrabs are everywhere, especially when they leap out at you from vents when you don't have your flashlight on. Compounded when the sequel added poison and fast varieties of headcrab. An unofficial design principle for custom maps runs thus: "A headcrab in every vent is boring; a headcrab in one-fifth of the vents is terrifying."
Adrian Shephard of Opposing Force definitely comes off as this to those wishing for him to finally make a reappearance ever since the G-Man put him in indefinite detainment at the end of the game.
Race X, also from Opposing Force, comes off as this as well to those who thought this alien race was more fun and unique compared to the Xen aliens.
The Nihilanth from the original game. Despite being the Final Boss and being built up to a lot throughout Xen, it's never brought up past throw-away lines by the Vortigaunts after the original game's ending. There's also everything involving the Nihilanth, from why it was trying to take over Earth to what it was running away from. Outside of the game's original ending, everything involving Xen besides the Headcrabs and Vortigaunts are either not mentioned or implied (but never stated). The theory that what the Nihilanth was running from was the Combine is never actually stated.
Lamar, Dr. Kleiner's pet headcrab. Every other headcrab is Nightmare Fuel defined and the only physical difference Lamar has from the rest is that she's been debeaked, but she's otherwise a domesticated pet who feeds on watermelons whose startling but completely harmless attempts to latch onto other people's heads and tendency to hide in vents is strangely endearing.