Games that actually make you feel for the characters...

[Jings]

Baldur's Gate 2 did a wonderful job of making you care about the characters I think. Everyone that joins your party has a well developed personality and they interact with one another in entertaining and sometimes moving ways. Fostering friendships and romantic relationships adds to the connection you feel with them and you really feel that they're not just there to hold a sword and carry your stuff, they're your character's friends and acquaintances and it really comes through in the game.

Putting certain character's with conflicting personalities and alignments in a party together also leads to conflict. The evil Dwarf and the goodly Elf obviously won't see eye to eye and the game makes sure to bring their differences to the surface and eventually force you to choose who you want to keep. This sort of thing has become a staple of BioWare's games but I think BG2 has the best examples of well developed characters that you actually care for.