Hmmm, I've been looking for a thread like this for quite awhile. The games I list go from my least favorite to my favorite.
Bioshock is my third favorite series. I'm not entirely sure what initially drew me towards the game, but whenever I play it, I can't put the controller down. I generally shut the curtains and turn off my lights and play in complete darkness. It makes me feel as if I am Jack (or Delta) and I'm actually moving through Rapture. It helps me hold my breath just a moment longer as I am about to turn the corner, awaiting a splicer to jump me. But Bioshock is more than just senseless murdering and shooting, it's a story of choices, of morals. Do you kill that innocent little girl in an attempt to further yourself? Do you save her? Every choice you make has a consequence whether you realize it or not. It's simple things like that - coupled by an amazingly thorough story background - that make Bioshock such an amazing game. In some cases it's overlooked because it's an First-Person Shooter, because some people generalize that all shooters are like Call of Duty, when Bioshock is clearly far from it.
My second favorite - but very close to first - is Assassin's Creed. I don't think I'll ever play a series that has made me laugh, smile, and nearly cry quite like Assassin's Creed has. I've always loved the stealth-based combat of Ezio and Altair; they are probably the coolest characters that I'll ever see in a game. They have such great emotion that you can't help but grow attached to them. I loved those two dearly even until the very end. The combat itself was also very good. The kill streak implemented in Brotherhood was very realistic and smooth; we could now do everything they showed us in the trailer just as quickly as he does it. With how smooth it is, I don't even feel like going through the motions as the player; I am the Assassin. All of this thrown together into an amazingly deep storyline makes it a must-play series. Requiscat in Pace Altair y Ezio.
And now for what should be a very obvious favorite; the Legend of Zelda. I've loved Zelda since I was about eight and I haven't regretted it once. Zelda is an amazing series that requires both fighting ability, and the ability to think in order to solve various puzzles that may be thrown at you. Various characters have also been quite intriguing, my personal favorite being the Happy Mask Salesman. I think that although Zelda has quite a bit of competition for first with Assassin's Creed, Zelda will always remain my favorite series.