Dating sims, or relationship simulation role-playing games (RS-RPG), are a video game subgenre of simulation games, usually Japanese, with romantic elements.
They are also sometimes put under the category of neoromance.
If you check here, there's a list (scroll down to the DS section) these are mostly dating sims for girls but some are for girls or guys.
Avoid the DS versions of Pets and Sims 3 like the plague.
Castaway is very fun but extremely short so it may not be worth the money.
The latest addition in this selection is Lord of Magna: Maiden Heaven released the 2 June 2015 It's time for classmating!
Monsters have invaded the world of Aterra, and only a few special individuals, imbued with the power of the Star God, are equipped to fight it.
There's actually a handful of them, but most (if not all) of them are in Japanese.
Sprung does fit itself into the "dating sim" category, but personally, I didn't like Sprung too much.Combine your Star power to make magical Star Children to boost up your forces in battle!Conception II: Children of the Seven Stars is a dating-sim JRPG (Japanese RPG) game where Dating-sim is an important part of the gameplay.There are games which offer "dating" as part of the game though and feature some relationship development, like The Sims, Harvest Moon, Rune Factory, and Lost in Blue 1/2/3 to name a few.Feel the Magic : XX/XY though not exactly a dating game, does have a plot involving wooing a girl, but sadly no real romance. The most common objective of dating sims is to date, usually choosing from among several characters, and to achieve a romantic relationship.