Dragon Age Origins
Silent Hill 2
To The Moon
The Walking Dead
Terranigma
Lunar 2: Eternal Blue Complete
Final Fantasy Tactics: War of the Lions
Borderlands 2
Batman Arkham City
As to what made me love these games... reasons vary wildly, but overall I think they are all at the very least above average in every one of their aspects (considering the time of release for production aspects like graphics). While there might be a flaw in the combat of it, the combat itself is not a flaw or a detriment to the enjoyability (unlike Alpha Protocol, PST), and while there might be a flaw in the storyline, the storyline itself isn't a flaw (Prototype, a blast to play, horrible story; FF8, usually FF games other than FFT don't have remarkable stories, but they are well done in what the want to be, personally loving 6 and 9 the most, but FF8's just got worse every disc.).
Same goes for presentation and music, etc. Basically, they are consistently good (great).
In terms of gameplay, I enjoy about everything, which reflects on my list I think. In cases like To The Moon and The Walking Dead, I specially liked the fact that they maintained the gameplay to the minimum, since it was obvious their focus was on the storyline and interactivity, and they didn't want to nor did lower the enjoyment by putting a lot of half-assed gameplay in the middle, but rather focused on the needed amount of gameplay at the right times.
As for plot-wise, a plot is needed for it to become my favorite, but it doesn't mean I can't enjoy something plot-less. Because damn if I haven't played my hundred hours of of Super Mario World, Tetris, and Killing Floor. Other than that, the storyline can be about pretty much anything, as long as it's well done in what it wants to be. Take for example Lunar 2, it's a very straightforward, classic adventure story that doesn't try to make itself into high art nor tackle social or human issues, yet it's very well paced, has a great cast, some really neat twists, and is just a very lovable story. On the other hand I can just as much love storylines like Silent Hill 2's that delve into humanity and are subtly developed. Or like To The Moon, that while not as narratively intricate, and more straightforward, it has just as much exploration of it's characters, emotions and human issues, and is more emotionally engaging, and even emotionally draining.
I can keep going for each of my examples but that would be boring.
You guys will probably notice the lack of Infinity engine games, but being honest, while I enjoyed BG series a lot, and IWD too (And... fighting through PST while enjoying the plot), they simply did not get in here due to the other entries. Still, regardless, I love me cRPGs, otherwise I wouldn't be here. KotoR, Arcanum, The Witcher, Elder Scrolls, Fallout, NWN, etc.
I know that feeling my man. ME was easily on my list, amazing cast in an entertaining storyline, with very good gameplay and fantastic presentation, and well damn near the top for most of ME3, flaws and all, but then that damn ending ruined the whole franchise for me. And unlike DAO, I can't take ME as three different stand-alone games.