Knights of the Old Republic did that to me hardcore.
I missed Jolee and HK-47 and Carth and Bastila and, and, and... Sigh. Well, everyone. It's like by the end of the game, all of the companions were this weird motley family I had grown so fond of. Ending that story was a bittersweet experience for me.
Dragon Age did that, too. My heart definitely tugged when everyone was saying their goodbyes and during the epilogue as well. I had learned everyone's stories by then with all of them at 100 approval, so I felt a solid, tangible connection between my elf and everyone else. Characters I wasn't fond of at first became favorites when I found out there stories and who they really were. I loved it.
Mass Effect was the exception to Bioware games making me feel a connection. I didn't feel like any of them were "family" or had bonded with each other the end of the story like in other Bioware games. They were just these people that followed me around unquestioningly and the only time they ever conversed with each other was through awkward and forced small talk in long elevator rides. Pretty disappointing experience for me. :/
Oh, and ending April Ryan's story in The Longest Journey was sweet and sad at the same time, too. I loved the conclusion, but I had grown so connected to her character that I hated to see her go.
