Oh shit, I didn't know Monopoly had such a strong plot... I guess I shouldn't have skipped all those cutscenes
Anyhoo, my favorite game of all time is probably the first Metroid Prime. I know, I know, not a classic 2D game, but I did find myself really liking that game, regardless of any engaging personalities. Other games I would rank up there would be Tales of Symphonia, LoZ:OoT, MGS, and Resident Evil (remake). Strangely, while WInd Waker isn't one of my favorites, it keeps on coming up in my mind whenever I think Zelda, thanks to the awesome style.
Character-wise, I like characters who are generally light hearted and sort of the comedic relief of the main cast. Zelos from ToS and and Sain from Fire Emblem 7 fit that description. I also really like the cast from the MGS series, and the character development of Garcian Smith from Killer 7, although those are probably strongly plot-related stuff, and less so regarding the personalities themselves.
Jam it back in, in the dark.