Although Karin is usually depicted as an only child of the Kanzuki family in most Street Fighter media (this is even stated as much in Sakura Ganbaru!), in the Ryu Final manga, she has three unnamed sisters.
Karin and Lili both have schoolgirls (Sakura and Asuka Kazama , respectively) for rivals, and declared them rivals soon after they were defeated by them; Karin was defeated by Sakura after a challenge, while Lili was defeated by Asuka at the fifth King of the Iron Fist Tournament.
Both developed their own fighting styles and enjoy the prospect of victory.
Both are somewhat selfish and stuck-up (but not really evil or malevolent) rich girls who come from wealthy families with companies/businesses being threatened in their main storylines.
Their butlers are present during their winning poses; Karin is shown with her butler, Ishizaki, while Lili asks her butler Sebastian if he can find a better person to fight than the person she defeated.
The comparisons come full circle in Street Fighter X Tekken, wherein Sakura compares Lili to Karin in the former's winquote against the latter.
In Street Fighter V, Karin's outfit design and fighting stance has a resemblance to Lili's.
The rivalry between them are completely different in their respective games. Both Karin and Sakura later became friends onward as their fight becomes more of a friendly rivalry while both Lili and Asuka remain dislike with each other onward as their fight becomes personal as seen in their endings.
Elisabeth Blanctorche from the King of Fighters series can be compared to Karin due their numerous similarities in character.
Karin and Elisabeth both have to fight off an enemy who is a threat to their family's foundations (M. Bison and Ash Crimson respectively).
Both have developed their own personal close-range fighting styles which involve high-speed hits and devote themselves to nothing short of absolute victory.
Both have butlers (Ichizaki and Jacques) who are utterly devoted to them and understand them more then other people.
Both come from rich and wealthy families of noble heritage/lineage with them as the only/sole heirs.
Both have strict and serious attitude from their upbringing and dedicate themselves to fulfilling a task once their minds have been set on it.
Both have been known to look down on those they see as lower stature or "commoners" and "inferior".
Karin also has a similar personality, mannerisms and background (including a nasty "ojou"-esque laugh) to Nanami Kiryuu from Revolutionary Girl Utena.
Karin is often comparable to Masashi Kishimoto's Naruto character Karin, who also happens to have a fighting rival named Sakura (though the latter case regards the kunoichis' infatuation towards fellow renegade ninja turned international criminal Sasuke Uchiha).