One thing that I am always glad to see is when game designers put in the effort to make characters, enemies, bosses, and NPCs more than just a collection of dialogue and basic statistics. One of the best ways to reinforce this is to give characters special statistics or AI routines that reflect their personality and individual character quirks. These kind of things can be small in the greater scheme of things, but can go a long ways towards making a character stand out in the player's memory.
This topic came to mind after I read some information on the recently released (in Japan) Super Robot Wars Z. In that game, every character has a bonus they give their squad-mates if they are the squad leader. One of the characters in the game, Kei, is a serious flirt and womanizer, so the game developers made his squad leader bonus a 20% bonus to damage when fighting men, and a 20% penalty to damage when fighting women. It is a small thing, but it suits his personality perfectly.
A similar example can be found in Final Fantasy 8, in the form of Raijin. When the party fights him in a boss battle, Raijin will generally not attack any female party member, thanks to a customized AI routine. This does a lot to reinforce aspects of his personality.
Another thing that I have seen done to great effect in various RPGs is giving characters specific characteristics or vulnerabilities that go outside the regular range of effects seen in the game system. For example, the is character in Wild ARMs 3 named Todd who has an Afro hair style. Todd also has the unique vulnerability that his afro can be lit on fire with any fire element spell, which causes him to lose hit points every round of combat. When I first discovered that quirk, I found it to be hilarious, and I still remember him for it.
A good example for traits like this in a non-RPG game is Metal Gear Solid 3: Snake Eater. In various boss fights, the player can draw out various personality quirks and vulnerabilities from most of the bosses. It is possible to impress Ocelot if you perform fancy tricks with the Single Action Army revolver. It is possible to distract and annoy Volgin in any number of ways, such as by throwing certain mushrooms at him. And most famously, it is possible to beat The End by letting him die of old age. All of these characteristics do a lot towards making these characters feel fleshed out and real, as opposed to just challenges dropped in the player's path.
I think that adding in small details like this to flesh out characters in a videogame is an excellent means of making a game more enjoyable and memorable.