The Hare Krishna appear as pedestrians in the first game (where you get a "Gouranga!" bonus for running down groups of them) and as one of the gangs in the second one, putting the "Targets" in Acceptable Religious Targets.
In the second game, saving your game requires you to tithe $50,000 to a church that's run by a Large Ham caricature of an American "prosperity gospel" evangelist. If you walk into the church without enough money, he'll yell "Damnation! No donation, no salvation!"
Vice City and IV make clear that Rockstar North are not very big fans of the Christian Right. Vice City has them represented by Pastor Richards, a crooked televangelist who keeps several mistresses and is funneling money from his ministry to build a mansion in Hawai'i, all the while preaching a warped parody of "prosperity gospel" theology that hails selfishness and greed — and, of course, generously giving a fair portion of your paycheck to Richards — as virtuous. In IV, meanwhile, Bryce Dawkins is the puritanical 'family values' deputy mayor of Liberty City who rails against anything that falls into his awfully broad definition of indecency, while also being a hypocritical closet case keeping up a secret relationship with Bernie (aka Niko's former brother-in-arms Florian).
Alternative Character Interpretation: It's surprisingly easy to interpret the GTA protagonists as vigilantes. When you think about it, most of their victims are criminals, serial killers, gang-bangers, mobsters, drug traffickers, corrupt officials, or terrorists. For all their evil actions, they do far more damage to the criminal underworld than the police ever did.
Anti-Climax Boss: Most of the bosses are very easy in comparison to the hordes of mooks you fight to get to them. Justified in that, while they may be criminal masterminds, they are still human.
Following GTA IV, the fanbase split into two directions — those who missed the more over-the-top style and player customization of the prior games (particularly San Andreas), and those who preferred the Darker and Edgier, more story-driven tone of IV. The Saints Row games briefly healed the fracture by causing some of the former group to gravitate to that series, but it split open wider than ever after GTA V came out and seemed to return to the style of San Andreas, causing an outcry from fans of IV.
There was also a brief split after it was announced that the protagonist of San Andreas would be a black gang banger from South Central, with many claiming that Rockstar was trying to pander to the tastes of pasty suburban white boys. However, that rift healed pretty quickly after San Andreas was released and the "ghetto" sections turned out to be some of the best parts of the game.
Epileptic Trees: Many of the explanations that some fans have given in order to support the idea that IV and Grand Theft Auto: Chinatown Wars are set within the same canon as the previous games, rather than an Alternate Continuity. Among them is the claim that there are actually two Liberty Cities, the one from III and the one from IV, explaining away the vast differences between the two depictions of the city. The fact that these cities and their inhabitants do not seem to have ever heard of each other, in spite of the fact that both are large cities located on the East Coast, and even when places like Vice City and San Andreas are frequently mentioned on radio and TV, doesn't occur to them.
Even though Word of God says the GTA1/GTA2 era, III era and the IV are three different universes, fans still apply characters from both in Fanfiction. Most intriguing are 1/2 and III eras which overlap often.
Goddamned Bats: Not literally, but Taxis and Police cars apply. The former can occupy the whole road at times (especially annoying during races). While tiny scratches on Police cars can make them onto your ass immediately.
Regular civilians also count since they have the tendency to hog the road, spawn in front of you while driving, jump into your incoming vehicle and make abrupt turns. Any one of these acts can jeopardize your current mission and they will do any of these acts randomly at any given moment.
Civilians on foot are not too smart in avoiding your car since they tend to dive into your path instead of away from it. At most, this is just a minor hiccup in your driving but at worst, this can happen when a cop is nearby and he'll chase you down because of the accident.
Ultracop. Due to a glitch in the game, some cops can simply teleport to your door and arrest you instantly. It has happened plenty of times in GTA 3 and VC, and he has also been spotted in GTA V.
Mexicans Love Speedy Gonzales: The original game was made by a Scottish studio, and the series is meant to be America from foreign eyes (which seems to be a Wretched Hive of a Crapsack World, of this series is any indication). That said, a good majority of fans of the series are American.
Narm: The excessive swearing present from San Andreas onwards sometimes makes the writing sound like it's trying to be edgy just for the sake of it — especially since Rockstar has a pretty good track record of writing dialogue that doesn't rely on constant swearing.
Never My Fault: The police departments (particularly in the HD era). Even after you hole up somewhere whose approaches become a Kill Zone, they neither change their tactics or recognise that your player character's death is not worth any number of theirs and back down. Not to mention that when there's potential for collateral damage or citizens are at risk of danger, they do not adjust for them.
Older Than They Think: GTA (the first one) was not the first open-world game. Zelda, for example, predated it by well over a decade, and there are probably some text games that are even older. Hell, GTA III is not even the first 3D open-world game; that honor goes to Body Harvest, a game that came out on the Nintendo 64 three years prior, and was in fact made by the same studio that made all the GTA games. One may argue that it was the first 3D open-world crime game, but once again, Driver, a game that came out in 1999 on PlayStation, beat it to the punch.
Similarly, people mistakenly thinking that the series began with GTA III, despite the rather obvious presence of the number three in the title.
Signature Song: "Grand Theft Auto" from the first game's hip-hop radio, N-CT FM, although it's not the Title Theme Tune, despite featuring a Title Drop. It is also confused with the instrumental main menu theme, "Gangster Friday". The hook from "Grand Theft Auto" is used as a ringtone in GTA III, Vice City and GTA IV.
Song Association: The games are very well-known for their soundtracks, particularly Vice City. Also, it's tough to listen to Lazlow's radio show without thinking of his work with the series.
Funny thing is, you can avert this trope in the PC games, which install a folder in your documents folder (where usually your saved games go), in which you can stuff as many MP3 as you want and/or recycle its content ever so often.
Grand Theft Auto IV: The story of two Eastern European brothers immigrating to America to escape their traumatic pasts as veterans only to get caught up in the criminal underworld evokes the Russian movie duology Brother. The segments with the Pegorinos, a Mafia family based in the suburbs of Alderney (an Expy of New Jersey), are heavily inspired by The Sopranos.
Grand Theft Auto V: The early parts of Trevor's story, which revolve around the meth industry in the southwestern desert, reminded a lot of players of Breaking Bad.
An inverted example with III. It's one of the few games that doesn't take too much influence from other media, but roughly a decade later the movie Drive would use a very similar setting, plot and main character.
Surprisingly Improved Sequel: III. The games before this were rather mediocre action titles that were only distinguished by their open worlds and controversial content.
That One Level: As good as the games are, each one has quite a few missions that are so frustratingly hard that they're sure to make you want to hurl the controller through the nearest window.
That One Sidequest: Paramedic missions. Completely optional, but doing them gives the player character a permanent health boost. You can't repair the ambulance at all during the mission, the slightest nudge can kill the people you're trying to save, and (until Vice City Stories) you can't save your progress — if you mess up on the last level, you have to start from the beginning! However, each completed Paramedic mission does restore the health of the Ambulance to some extent, making life a little easier.
What Do You Mean, It's Not for Kids?: It is amazing and disgusting how many parents think it's fine for their kids to play GTA. A personal favorite parental defense: "Grand Theft Auto is the only M-rated game we let him play."
Conversely, most of the controversy surrounding the game stems from this trope being applied to video games as a whole. Moral Guardians think that only kids should play video games and therefore making one about violent crime is absolutely heinous.
One of the highlights of the past was in 2004 when an 85-year-old New York grandmother that became upset that she bought Grand Theft Auto: San Andreas for her 14-year-old grandson (she did have the game taken away from him) and launched a lawsuit against Take-Two over it.