Aside from my love for The Sims
because I really get a kick out of playing god, and Pokémon
because it was my childhood-defining game, I'd say my favourite is SMT: Persona 3 Portable
I haven't played the original PS2 game so I can't really compare the two, but the remake is pretty damn awesome.
You get to play as a female - which, aside from appealing to female gamers, offers a completely different perspective on the plot as her personality and interactions are different from the male main character's -, and the game is this wonderful mix of elements reminiscent of: Pokémon, what with Tartarus being the dungeon and having turn-based Persona (kinda like your pokémon only they're technically a manifestation of your psyche) battles against Shadows, plus you can fuse your Personae to obtain more badass ones and you also have a compendium (read: PokéDex) to complete by collecting all the Personae; dating sims, as you have to improve your stats and the bonds you form and deepen with others influence your Personae but also give you the chance to date several characters at once (seriously, both MC and FeMC are frequently dubbed 'pimp' and 'pimpette' by the fanbase); apocalyptic end-of-the-world madness, complete with friend-turned-harbinger of tragedy and all. More on that in the spoilery rambling below:
[spoiler]It's hard for me not to liken Ryoji to Kaworu in a few aspects, not counting the ikemen-ness: both are around for a short amount of time, aren't entirely human, bond with the protagonist fairly quickly while declaring their affection for him/her, have the drive to return to their parent entity and said entity would bring about the end of the wonder and consequently extinction/restart of life, and ask the main character to kill them for the greater good.
Also, Aigis is wary of Ryoji, just like Rei was wary of Kaworu... Aigis being a cute emotionless robot originally made to destroy shadows, but who ends up 'becoming' much more human through her interactions with the protagonist. Oh, and just for kicks, Akira Ishida voices Ryoji in the original JP version.
There's also some interesting babble about the will to live vs mortido and sacrifices that must be made for the greater good (mostly at the end of the game), and good amounts of fanservice as you can dress up your female party members in skimpy bikinis and maid outfits and your male ones as butlers. Most of the characters you interact with have their own personal little dramas and issues going on, which I found highly entertaining. Still, don't think you have all the time in the world to take your relationships to the next level (literally speaking), as you only have one in-game year to max them all out before [s]3rd Impact[/s] doom occurs, and as if that weren't enough to keep you busy, there are still some optional quests you can take for rewards.[/spoiler]
Lastly, shooting yourself in the head to summon a Persona makes throwing a measly pokéball look as cool as a slimy, flaccid worm. Everyone should play this game just for that.