Well, I differ in opinion. For me, true RPGs are Pen & Paper Role-Playing Games such as Dungeons&Dragons or Vampire: The Masquerade. To play them, you doesn't really need computer, you just meet with your friends and every one is "playing" his own character. Each one says what say his hero and describe what he or she is doing. One person is the Game Master (or in D&D Dungeon Master) - his role is to keep everything running smoothly, master the story and play for all background characters (also called NPC).
I hate when somebody says that Neverwinter Nights, Baldurs Gate etc are RPGs. They are just cRPGs - computer role playing game. If you want to play true role play, go to some Fantasy Fan Convention and I promise you won't be dissapointed
And so I also very like computer games that places strong accent on story and atmosphere. For example I played once Neverwinter Nights 1 multiplayer on polish role-play server and during 8-hours of game I didn't kill even single monster. And it was real fun, as one of the most experienced player was mounting a party which lasted from 4PM to 12AM. We singed, danced and were chatting and I met a lot of great people.