I have a soft spot for games where you build your party members. For example, the Final Fantasy Tactics games and all similar games usually allow you to recruit arbitrary characters to fill your party out. Many Dragon Quest games also allow you to build characters.
There are a few downsides to this, but let's stick to just two:
1) There is a very uncomfortable relationship between created NPCs and scripted NPCs. Scripted NPCs tend to be more powerful and have unique abilities, meaning that the characters the player spends the most effort creating are also the weakest. That's bad. Also, from the other direction: scripted characters tend to not change visuals to match class changes, so it's hard to remember what role the scripted characters play.
Games where you can create NPCs would benefit from not having scripted party allies. This can be done by either having no plot-entangled party members (such as some Dragon Quest games) or by making the plot elements attach to arbitrary NPCs you've created instead of actually linking to a scripted character.
2) NPC creation is usually pretty painful. It either features some kind of extremely generic creation screen (class, name, gender) or an awkwardly over-detailed randomly rolled set of stats (oh, should I reroll so that my AIM is 81 instead of 79?)
If I want to feel attachment to these characters, rather than that method, I propose a "talent" system. Instead of randomly rolling ten different stats, randomly choose three tiered talents and two visual perks. Talents would be things like "beefy" or "cunning" or "ice-element aligned". Visual perks would be things like "messy red hair", "glasses", "long face", "curly beard"...
This combination means that you'll be able to remember the character more easily and not lose track of their specialties in a mess of ever-changing numbers. When the character changes job classes, they don't magically lose all their unique visual elements. Instead, they simply change outfits but remain with the same palette and fundamental visual characteristics, allowing you to remember who someone is even after they change jobs.