Mass Effect 2.
When I first played the original Mass Effect, I couldn't get into it at all. Everything about it was clunky and awkward. The voice acting, the equipment menus, the controls, everything.
When I picked up Mass Effect 2, I found that literally ALL of these issues had been fixed. The engine, the menus, the voice acting, the body language of the characters, EVERYTHING was so much tighter and more fluid and more natural, and so I could really get into the game. I loved it so much that I went back and gave ME1 another try, and finally finished it, and even though I still don't actually like ME1, I'm glad that ME2 convinced me to give it another go and see it all the way through, if only so I could have Wrex alive in ME2 and ME3.
Also, I fucking loved ME3. Fuck the haters; a half hour of mediocre writing at the end does not in any way devalue the 20 hours of fantastic writing and gameplay that precedes it.