He is a parody of Richie Rich, but unlike Remy, Richie Rich is a genuinely kind and friendly person (despite his rich lifestyle).
Remy since his first appearance has been shown to be a sympathetic antagonist due to his parents neglecting him just like Timmy's. However, his most recent appearances (like Country Clubbed) depicted him as a pure antagonist due to his hate for Timmy.
Because Remy has not appeared from season five until season nine, and Juandissimo was competing in the Fairy Idol contest, it was widely assumed that Remy lost Juandissimo as his fairy, especially considering his behavior in "Operation F.U.N.". However, "Teacher's Pet" reveals that Remy still has Juandissimo as his godparent. Strangely, he did not appear in that episode.
His parents only spend 2 minutes a day with him and not only forget his name, but forget he's their son.
Remy and Timmy had a truce at the end of The Big Bash! due to Cupid tricking both of them. The same truce is broken in Operation F.U.N. by Remy.
Remy appeared in the episode Country Clubbed. This is his first physical appearance in the series since season 5, before Sparky and even Poof were added to the main cast of the show. Starting with Season 9, Remy has a slightly different hair style.
Remy Buxaplenty is similar to Squilliam Fancyson from another Nickelodeon series, SpongeBob SquarePants. Both Remy and Squilliam are rich, are arch-rivals with main characters (Timmy Turner and Squidward), and are both voiced by Dee Bradley Baker, however, Squilliam has lots of friends, while Remy has little to no friends.
His surname is a pun on "Bucks a Plenty". In Latin American Spanish version the pun is translated Cajallena (Caja: Box, Llena: Full). In Spanish, Cash register is Caja registradora (Box register), and Savings bank is Caja de ahorro (Savings box). Maybe in one of these two expressions is the joke of the pun in the Remy's Spanish surname.
Some fans have paired up Remy with Trixie Tang as his love interest, since they're both wealthy and snooty. However, in the episode where they did appear together, "Remy Rides Again", neither Trixie nor Remy interacted with each other.