1. Gears of War
2. Fallout
3. Halo
4. XCOM
5. Bioshock
6. Mass Effect
7. Max Payne
8. Fable
9. Dragon Age
10. Silent Hill

1. Age of Empires
2. Call of Duty
3. Fifa
4. Gran turismo
5. Uncharted
6. Yugioh Games
7. Mario Kart
8. Battlefield
9. F1 Games
10. One Piece Games

Deus Ex

Thief

Max Payne

Hitman

Batman Arkham

Heroes of Might & Magic

Carmageddon

SSX

FlatOut

Dirt

There is no doubt that AS/OM and sun/moon could've been better, but the series is still something which consistently pushes out games worthy of 80-88ish, which is why I give it recognition.

The 3ds is laughably weak, and it's obvious they wanted to truly expand the game. Nintendo is improving many of your IP's, so don't be too worried about the series.i know you disliked sun/moon, but the Switch titles will hopefully allow the new director to do what he wanted

Excluding almost all P&C Adventures and IPs with less than 3 entries, in no particular order:

Might and Magic
Gothic
Fallout (excluding FO4)
Tomb Raider (pre-reboot)
Combat Mission
Zelda
Myst
Souls
Warcraft (RTS)
TalonSoft Battleground/Campaign series

Interesting thread. My 10 favorites (no particular order)

Shin Megami Tensei
Fire Emblem
Super Mario
The Legend Of Zelda
The King Of Fighters
Animal Crossing
Professor Layton
Resident Evil
Street Fighter
Splatoon

Honorable mentions: Castlevania, Donkey Kong, Bayonetta, Tekken, Ace Attorney, Pokemon

Let's see then.

1. Final Fantasy
2. Dark Souls/Bloodborne
and the rest in no particular order because I couldn't decide
-Tekken
-Command & Conquer
-The Legend of Heroes
-Uncharted
-Valkyria Chronicles
-Metal Gear Solid
-Mario (platformers)
-Kingdom Hearts

Updating my list

I am silly and forgot a big one, Dragon Quest!
And one kind of big one, Soul Blazer.

In addition, my ordering was a bit weird. I didn't put enough thought into it. While Xenogears is my favourite game of all time, there are no other Xeno games I can put in my top 10, even though all of the Xeno games make my top 50. I don't think I have gone a single season of any year since about 1988 or so where I have not played a core Mario game, or one of its many spinoffs. I can't even say the same about the Xeno franchise which began in 1998 - and currently amounts to only 6 games - against the, maybe, 50 Mario games I own. With multiple series of games and spinoffs that I love: Mario Galaxy, Mario Bros, Mario Kart, Super Paper Mario, Mario RPG, Yoshi, Dr. Mario, Mario Party, etc... no other franchise is so heavily represented in my library, so Mario is a clear number 1.

I am mostly going by the number of games I enjoy in the franchise, and the amount of time I put into games; franchises like Pokemon, Shin Megami Tensei, Disgaea, and others, require lots of time to get the most out of the games, but I find with all of those I have a tolerance of no more than about 35-40 hours, and then I feel like I am wasting my life. Xeno, Dragon Quest, Zelda, Harvest Moon, and Paradox grand strategy games are the only franchises I have put 100+ hours into one playthrough... and with those, I always considered high quality gaming time. Breath of the Wild is my first 100+ hour Zelda, I have played them all (minus the licensed out games).

I would love to put Resident Evil, Castlevania, Breath of Fire, Suikoden, and others, but each has issues. Resident Evil, I only really liked 1-3, and only liked 4 because of the Wii controls, I don't enjoy it at all without IR aiming. Castlevania, I was a big fan of all the games from the beginning, but especially Castlevania 3, Super Castlevania, Rondo of Blood, Symphony of the Night, and Circle of the Moon; I did not enjoy any post-Circle of the Moon, each game afterwards felt like it was falling more and more behind gaming trends, and they lacked the spirit of earlier games. Suikoden, I feel the same as Resident Evil, while I love 1 and 2, the remainder of the games felt a little weak to me. Breath of Fire and Lufia, games like that, I have always enjoyed, but have found every game in those franchises tend to have too many imperfections. Lunar, Earthbound, and others are like Suikoden, too few games I enjoy. Soul Blazer is just a trilogy, but I replay all of those games to this day, and would put all three games in my top 20 of all time, only bonus points for tacking on related games like ActRaiser.

Unfortunately, I have to say goodbye to Animal Crossing and Ace Attorney on my list; they got pushed off.

1. Mario
2. Xeno (gears, saga, and blade)
3. Dragon Quest
4. Zelda
5. Final Fantasy (only 1, 3-8, Tactics, X, and the gameboy games that are technically other franchises)
6. Soul Blazer (Soul Blazer, Illusion of Time, Terranigma)
7. Paradox grand strategy games
8. Harvest Moon (now Story of Seasons and Rune Factory, screw Natsume's current "Harvest Moon" games)
9. Fire Emblem
10. Kirby

Well, the Switch has been doing well in terms of improving franchises. I'll be optimistic surrounding Prime 4 and Gen 8, but we'll see what happens

in no order

1. sonic
2. megaman
3. kirby
4. donkey kong
5. street fighter (including vs series)
6. resident evil
7. kingdom hearts
8. phoenix wright 
9. Smash bros 
10. pokemon

EDIT

11 Assassins creed
12 Animal Crossing
13 Mario kart
14 zelda
15 metroid
16 dragon ball z
17 fire emblem
18 star fox
19 Harvest moon / Story of seasons
20 advance wars

had to re think this