Mass Effect - whole series. From the imperfect combat of the first through the drawn out middle act of the second through to the heart-breaking ending of the third which still leaves me feeling a little hollow inside, I love every moment of it, flawed or not. No group of characters has ever reached me like the extended crew of the normandy and never have I been able to insert myself into a protagonist like I have with commander shepard. I have countlss completed playthroughs and although I always make similar choices, each of my shepards has told a slightly different story.
The Elder Scrolls IV/V - First Oblivion and then later Skyrim ate my life for a few hectic months before I was finally done. I can keep going back to both, even if they don't suck me in like they did at the beginning.
Portal/Portal 2 - There are few games that tell a compelling story through a silent protagonist. I normaly hate silent protagonists. Valve once again make the exception that proves the rule, like Gordon Freeman before her you care about Chell and what happens to her in this insane world of SCIENCE! Also need to mention Glados and Cave Johnson; an antagonist that you grow to love for her sadistic psychopathic nature and a character who exists mainly to drive the backstory of the antagonist who made me cry with laughter.
Assassins Creed - Series gets a slightly tentative entry bcause of its ups and downs. Personal favourites were ACII and Brohood. However, though I felt the story and protagonist of ACIII were flat to the point of boring, I LOVED the naval combat and am therefore going insane in anticipation of ACIV...
Guitar Hero - My guilty pleasure, I own 5 of the series, Warriors of Rock was by far the best IMO, but the series finally coaxed me into buying a real guitar and learn it with Rocksmith, which isn't on this list but gets an honourable mention here because of its patience with me...
Minecraft - Easily my favourite Indie success story, Minecraft is probably responsible for the most sleepless nights on this list, bar ME perhapse. when you get gripped by a project or an idea, a new concept you want to test out, it can be hard to tear yourself away. The only serious problem is you spend hours upon hours building your perfectly designed boat or castle or cathedral, then you go and look up similar projects on Youtube and then hate yourself...
There are other games that have kept me engaged during this generation, but those above captured my immagination best. These are very different worlds in which you can loose yourself, be someone else or are just so abstract that you can remove yourself entirely.