Up to this day Bastila from The Knight of the old Republik is one of my most memorable companions. Thanks to her I actually had my first "real" emotional moment in a pc game.
In my first playthrough I was (of course) being a good and shiny hero. So we bonded and everything was going fine until she was captured by this sucker Malak. And he started turturing her. That mofo! I was really sitting at my desk in anger and sweared to kill him for killing my beloved Bastila! Imagine my pure joy when I landed on some port and saw her in the distance! Alive and as beautyful as ever! Wohooo! So I ran to her and was totally and utterly shocked to discover that she had turned to the dark side! That is until today one of the most impressive moments a PC game created for me. Eventhough I was well aware that it was just a game and that I was just following a storyline on the cognitive level it got me deeply involved on an emotional level and for the rest of the game I desperately tried to "save" her.
In contrast on my second playthrough as The Lord of Evil I was happy to have a pretty chick beside me that I could rule the universe with.
I also still remember Mafia (the good 1st part) when I was walking home Sarah and in this dark alley we were approached by this bunch of thugs. I was not only beating them up, because the game mechanics wanted me to. I was beating them up to protect her.
So I guess what is working for me very strongly to get involved is to appeal to my protective instinct.