Well instead of naming mainstream series/games... I will go with Games and series really not known or played that deserve some Luv...

Zero Escape Vol 1: 999: 9 Hours, 9 Persons, 9 Doors and it's sequel Zero Escape Vol 2: Virtue's Last Reward(NDS, N3DS/PS Vita)- Best Video Game story I ever experieced in 999, plus a killer soundtrack and memorable characters. VLR story and OST is also gold and the Characters cast is strong as well, and improved gameplay and graphics over the first one makes it the better of the two games. Not to mention both stories have more twists and turns than a game of porno twister... If you like visual novels/solving puzzles look no further... these are your holy grail of games.

Castlevania Dracula X Chronicles (PSP) - A remake of the Classic Castlevania: Rondo of Blood and does it justice with better graphics,  voice acting and animated intro. The biggest improvement from it's predecessor is the soundtrack that'll make you cut up wooden broomsticks, make a wooden cross and REALLY become a Vampire Hunter. Oh and it has the OG Game AND Castlevania:Symphony of the Night as well. Best $10 I ever spent in my life.

Fire Emblem: Path of Radiance and Radiant Dawn (and pretty much the whole Series) NGC and Wii) - Sure Radiant Dawn is an acquired taste but if you enjoy a challenge while testing your stragetic wits along with memorable dialogue and characters, look no further (plus comes closest in creating a Medival Darth Vader). Radiant Dawn is rated low unjustly by critics because of the supposed inferior graphics from PS3 RPG titles and difficulty. The whole Fire Emblem series is underlooked in paticular. More gamers should know about the exploits of Ike, Lucina, Hector, Lyndis, and Marth.

Anybody else have any recommendations?

I, for some strange coincidence, had the pleasure of playing 999 and Ghost Trick at the same time. Both mindblowing games with mindblowing conclussions. So since OP recommended 999, I strongly suggest giving Ghost Trick a chance.

The Dead Rising series. Especially if you love zombies, wacky-but-dark humour, some touches of drama, silliness and gore. This series is so incredible fun. Minus Dead Rising 3, that one is a bit disappointing in comparison to the other two (Still great, though!)

Serious Sam. Awesome "modern" FPS with every ounce of old-school spirit.

Trauma Center games are interesting. They not only offer a challenging but fun gameplay, but also goes their way to introduce the player to a mythological plot full of twists and things. Check it out!

Max Payne trilogy, because yes. Nothing like noir drama with the ability to make time go slower.

Hmm... Thanks for letting me know about Ghost Trick. Seems like it has the same gameplay as 999 and is also made by Capcom (probably my 2nd Fav game maker).

Also always wanted to get into the Dead rising series but my back log doesn't permit me to... :-/

Atelier series (JRPG)

The Wondeful 101

Okami

The Last Guardian

Final Fantasy XV

Silent Hills

Not sure if joking or you don't understand the title.

OP: Hmm. That's a tough question. I'll go with recent games since they are more fresh in my mind. I'll pick two games. One of them lesser known and one more mainstream. 

Lesser known - Prince of Perisa (2008): Honestly; I might be exaggerating, but this game changed my life. It just made me feel happy. Playing through the watercolor-like world was a beauty of it's own. Voice acting and platforming were superb. Different from the other PoP games, but I never played those anyway. If you can go into this game with no expectations and just enjoy collecting and experiencing a beautiful realized world, I really think most would enjoy it. 

Mainstream - Mass Effect Series (2007-2013): Okay this one didn't change my life, but the story and characters had a long lasting positive effect on me. The relationships you form in the series from the first to the final game are the BEST in the video game industry; bar none. It's honestly not even close. No other series has created meaningful fictional relationships like Mass Effect has. I played through the entire series twice with at least 200 hours total spent. Loved these games. The world and information/fiction Bioware created... Truely breathtaking. Honestly I could spend hours just listening to the codex. 

If this thread is about games you must play before dying, then I pick those so that I will live forever.

These are franchises I enjoy the most and would recommend them to everybody:
Tomb Raider
Grand Theft Auto
Far Cry
Resident Evil
Borderlands
Uncharted

I don't care that they are mainstream, those are the games I could always play.

Persona series.
The Last of Us.
DanganRonpa series.
Valkyria Chronicles 1.
Dark Cloud 2.

Aaaaand... this just turned into a list of my favorite games. Still, everyone should play all of them.

It could also be a favorite games list too... but I pretty much narrowed it down to games I've played and found unexpected gems. For instance, never played any Zero Escape game beforehand, but now it's my 3rd favorite series.

Valkyria Chonicles is a series I wanna get into soo badly as well... I own all three games but work, hobbies, other games have me tied me down to start any of them.

I could have recommended everyone to play my favorite game series (Zelda, Street Fighter, Resident Evil, Pokémon) but I bet people are tired of others recommending those series! Least your game list isn't so mainstream.