Awesome Art: Akira Noguchi's concept and promotional art uses a strange, very unique, very colorful style that looks wonderful. The sprites are also some of the most popular in the Mario franchise, to the point that it's popular to customize them.
While Bowser's depiction as one of the protagonists in Bowser's Inside Story is universally loved, fans are divided on how he's depicted in the rest of the series. Bowser goes from an Ineffectual Sympathetic Villain and Butt-Monkey in Superstar Saga and Partners in Time to a Knight of CerebusBig Bad in Dream Team and Paper Jam. Both portrayals have their fans, who frequently argue about which characterization works better for the Koopa King.
The relative quality of the games. Which one is the best and which one is the worst? The consensus seems to be that both Superstar Saga and Bowser's Inside Story are the two best games in the series, and fans debate which one of the two is the best of all. Opinions on how the other three games measure up are all over the place, but consensus seems to be that Dream Team and Partners in Time have mixed reception while Paper Jam is So Okay, It's Average. However, most fans agree that all the games are at least good and enjoyable, unlike its sister series, which is widely seen to be going through a Dork Age nowadays.
Contested Sequel: Every game after Superstar Saga with the exception of its own 3DS remake and Bowser's Inside Story, which is seen either as an Even Better Sequel or in the same league, has been met with this.
Partners in Time got it mainly because of its extreme linearity, overly long boss battles, replacing Bros. Attacks and Points with Bros. Items, total lack of post-game content, and more. In spite of this, many like the idea of having four characters in battle as opposed of two like in most other games, and the linearity can make the game faster-paced compared to others.
Dream Team was this to Bowser's Inside Story, mainly due to its slow pacing and excessive Forced Tutorials, although the latter has always been a problem in the Mario & Luigi series (that said, Dream Team is the worst offender in this regard). Other reasons include the fact that Bowser is the true main villain after being the main protagonist in the previous game, with the supposed main villain Antasma being a Generic Doomsday Villain, or the sometimes broken gyro controls, something that the next game removed entirely. However, some would argue that Dream Team has the best gameplay in the series, with many of its boss fights being some of the best, that it has some clever use of the dream world mechanics, great level design, the best soundtrack of the series, and the fact that it still had unique characters and locations as opposed to the approach followed by many recent Mario games.
Fawful is one of the most beloved and quoted characters among the Mario fanbase for his hilarious personality and speech patterns.
Bowser. The first two games (especially Superstar Saga) give him the short end of the stick, but his playable role and ridiculous feats in Bowser's Inside Story are well-loved, and subsequent games let him keep the levels of badass he took and turn him into even more of a Knight of Cerebus than he is in the main platformers while keeping him as hilariously hammy as always.
Fandom Rivalry: For a long time, fans of both Mario & Luigi and Paper Mario were Friendly Fandoms, in no small part thanks to both series having several similarities while being different at the same time. That was until Nintendo revealed that they were planning to make Mario & Luigi the de facto Mario RPG series, and Paper Mario would continue in Sticker Star's direction, saying that Paper Mario wouldn't need RPG elements since the former "already covered those" (which is pretty ironic given that the Mario & Luigi series incorporates platforming elements into its gameplay a lot moreso than Paper Mario). Now Paper Mario fans often argue that Mario & Luigi can't replace the former, among other things. This is a somewhat subdued example, as due to a significant overlap in both fandoms, not only do Paper Mario fans not actually dislike Mario & Luigi fans, but fans of Mario & Luigi also disagree with the idea of "already covering" the RPG audience. It doesn't help that each series are noticeably different in formula, making the statement about not having two Mario RPG series even more controversial. Additionally, both series would end up in the same position of unsure futures after having major sales flops around the time Nintendo's Nintendo Switch sparked a transitional period for the company.
First Installment Wins: Despite the sequels developing on and streamlining the gameplay further, many people still cite Superstar Saga as the best one in the series. On the other hand, many fans consider Bowser's Inside Story as the best one, or at least second to Superstar Saga, in no small part thanks to the improved gameplay, Fawful as the main antagonist and of course, Bowser as the main character.
The series never really had many interesting Toad NPCs, there may have been Toadbert, Toadiko and Doctor Toadley, but that was it. Most were just the standard multicolored Toads, and by Dream Team the standard multicolored Toads were the only Toads to speak of, outside a token appearance by Toadsworth. This was mitigated by the fact that there were other interesting and unique NPCs that were unique to the series. Paper Jam does away with the unique NPCs and has most of the NPCs be generic Toads or Paper Toads.
The series' lack of innovation between games wasn't a big issue early on when budgets were smaller and each game could be carried by its unique theme, writing/characters, and gimmicks. This ended up causing issues starting with Paper Jam, which despite still being a fun game had a more generic feeling to it compared to the first four due to the restrictions it was held to, so it didn't get much attention. With the following two games being remakes instead of wholly new titles (and being on the 3DS, which was quickly losing relevancy), it was easy for players who had already jumped ship to pass them by, and the increased cost of making 3DS entries didn't do AlphaDream any favors.
Also, Bowser complains about fat jokes when he gets stuck in a Bullet Bill blaster in the first game. A major plot point in the third game has him gaining weight from overeating.
Magnificent Bastard: Fawful initially served as The Dragon to Cackletta in the first installment, where he brainwashes the Koopalings and other minions to work for her in Minion Quest: The Search for Bowser. After Cackletta's defeat, Fawful becomes the Big Bad of the third installment. First, he sells a sinister mushroom to the Toads of the Mushroom Kingdom, a mushroom causing the Blorbs. When the leaders of the kingdom get together to ponder the dilemma, Fawful gives the defeated Bowser a Vacuum shroom causing him to inhale everything in sight. Upon taking over Bowser's castle, Fawful brainwashes Bowser's loyal minions to take over the castle, create a theater, and fatten Bowser up; upon him reaching the castle. This is to extract Princess Peach from Bowser's body, which he uses to awaken the Dark Star giving him total control of the Mushroom Kingdom. As a last ditch effort, when Bowser finally makes it to Peach's Castle and after Bowser inhales the Dark Star, Fawful, after being defeated merges with the Dark Star and creates Dark Bowser to fight Bowser and Dark Fawful to fight the Mario Bros. In spite of conquering the Mushroom Kingdom, Fawful is a Noble Demon and has a soft spot for the baby versions of the Mario Bros.
Tough Act to Follow: While nowhere near as bad as in its sister series, some fans believe that every game after Superstar Saga has failed to reach the same level of quality. Likewise, some feel that Bowser's Inside Story was the series' high point, and that both Dream Team and Paper Jam were disappointing successors to the the third game. Downplayed, however, in that the games were still well-received in spite of this, unlike the Dork Age caused by the later Paper Mario games.
The Woobie: Luigi, definitely. This scene and this scene from Superstar Saga and Partners in Time respectively, increase Luigi's woobieness when he breaks down crying in both of them.
The games are known for diverting drastically from the Japanese scripts whenever Rule of Funny comes into play. The Hammer Bros. in the second game in particular definitely did not speak in 1337 in the original.
Fawful is interesting here, because he talks in a different funny way in every single translation. He adds Ru to the end of every sentence (repeatedly) in Japanese, has mangled Engrish in English, a strong accent in French, stutters in German, uses made-up words in Italian, speaks the same in American Spanish versions, and speaks in refined Spanish with set phrases in the European Spanish versions. He speaks in metaphors in multiple versions.