I'll always vouch for Persona 3 for a plethora of reasons, from the theme of the game to the symbolism to the likability of the characters (can't really go wrong with Shin Megami Tensei in general).
That's my top pick, but in no order my others are:
Danganronpa: Trigger Happy Havoc has a fantastic premise and storyline overall. Plays a lot like Phoenix Wright with the visual novel elements of Persona 3/4.
I thoroughly enjoyed Bioshock Infinite. People praise 1 but it's a bit overrated, and has a totally predictable outcome.
Silent Hill always has outstanding storytelling.
Grand Theft Auto always has outstanding storytelling.
It's a love it or hate it kinda deal but, the Metal Gear series is extremely entertaining.
I Have No Mouth and I Must Scream, albeit bleak is excellent for what it is.
Grim Fandango is an awesome point/click.
Brutal Legend is amazing provided you appreciate metal music.
Deus Ex is cool.
Iunno, anything else I'm missing?