@OP First off, why wouldn't you include Nintendo? I suppose I'm missing some kind of anti-N bias.
Anyway:
Microsoft -
Null. Sorry, their franchises have just never appealed to me, unless we're talking about old PC games. I have never been attracted to the Xbox brand.
Sony -
Jak & Daxter (though I really wish they'd take the series back to it's roots and make a new entry like the first game. I really felt 2 & 3 were hot garbage, straying from what made 1 unique, and instead trying to cash in on GTA's success, which was stupid.
Team Ico Games - I really liked Shadow of the Colossus, and I REALLY wanted to own The Last Guardian for PS3. Too bad that's not gonna happen now. At this rate, it's questionable the game will ever even come out on PS4.
Crash Bandicoot - I liked the original PSX Crash games, they were fun. In all honesty, I liked the two Crash games that came out on Wii in the last few years as well. But as far as "exclusive" games goes, the old Crash games were cool.
Nintendo -
Mario - I haven't loved EVERY single "main" Mario entry that's come out. I have never liked Lost Levels, I'm personally glad we got "OUR Mario 2", I just never cared much for Sunshine, and I felt Galaxy 2 was unnecessary and not nearly as good as Galaxy 1. But otherwise, I've loved most of the Mario titles, most especially SMB1-4 (3 being my fav.), 64, Galaxy 1, NSMB Wii & U, and recently 3D World.
Zelda - Again, I haven't loved every entry. I've never gotten into any of the portable ones beyond Link's Awakening, which is still arguably my favorite old school Zelda game. I also hated Majora's Mask, and could just never get into Wind Waker. I love Zelda 1 and 2 on NES, ALttP is an obvious classic, Ocarina for it's time was amazing, and Skyward Sword was very flawed, but I still mostly enjoyed playing it beyond it's frustrating over-use of motion controls for everything. Twilight Princess is still the best 3D action/adventure game I've ever played thus far, and thus obviously the best 3D Zelda IMO.
Metroid - I've liked pretty much every Metroid game to come down the pipeline, even though I didn't really get that into Prime 2, until Other M. That game is an abortion, and Nintendo should have never allowed a hack outfit like Team Ninja to work on one of their most beloved franchises. Otherwise, Metroid, Super Metroid (Metroid 3), Zero Mission, Prime 1 and Prime 3 are all great.
Kirby - I've loved Kirby ever since I played Adventure on NES. And oddly enough, unlike the "big three" mentioned above, even though I certainly have entries in the series that I prefer over others, I can't think of any Kirby game I really DIS-like. Adventure on NES is still my favorite, though the two on Wii were both great in their own ways.
Mario Kart - One of my fav. racing franchises, and sadly the only one left that is really much good (I stopped liking the new Ridge Racer and Need for Speed games several years ago). Still, I absolutely hated Double Dash, and while Wii had some good things going for it, the exploitable nature of the bikes and the unbalanced power up situation really soured me on that game. Mario Kart 64 is to this day the best in the series to me, but I have hope for MK8.
Smash Bros. - The first game was a neat curiosity, though the only real appeal was in multiplayer, as the single player mode just didn't have much too it. Melee was a great step forward, with an adventure mode and more characters. Brawl totally blew it out of the water, IMO, and I personally really loved the adventure mode in that. I hope the new one is even better, though I have some reservations about what Sakurai is going to do with the new adventure mode.
Wave Race - I have loved this entire series. The original Game Boy game doesn't have much to it, but the N64 game blew my mind when it came out, and the GC game was a nice follow-up. I really am holding out hope for a gorgeous looking HD Wave Race on Wii U.
Star Fox - The SNES original was good, but I never got THAT into it. The N64 game on the other hand, is still one of my favorite games of all time. Which makes it that much shittier that Nintendo hasn't put out a GOOD Star Fox game since. I really wish they'd just get the team that made 64 back together and have them make one again.
F-Zero - Never one of my favorite series, but I do like it alright. F-Zero X was a lot of fun on N64, and GX on GC was also good, but too damn hard. It would be cool to see a new one, so long as they balanced it out a bit.
Pikmin - I have absolutely loved this series since the first game came out. 2 improved on it in a lot of ways, even though some of those underground areas are outright murder. I waited a damn long time for 3 to happen, and when it finally came out, while it certainly is a good game with a lot going for it, there were certain key elements that makes Pikmin PIKMIN that they mysteriously decided to change/omit, and I couldn't help but feel disappointed in what otherwise could have been an amazing game. I hope that maybe if they make a 4 they'll make it the way it should be, like the GC ones.
I have other Nintendo franchises I like, such as Paper Mario, Star Tropics, Punch Out, etc. But those are the main ones I like the best. In general, that is the #1 reason why I have stuck with Nintendo well into my adult years, because unlike all the other companies I liked growing up, that USED to put out high quality games, such as Square, Enix, Capcom, Namco, Midway (dead), Hudson Soft (dead), Konami, Sega, etc. Nintendo is the only one left from that old guard that still consistently puts out games that I actually want to play, and that are actually fun to play.