2nd Generation - Atari 8-bit (especially XEGS):
I didn't grow up in this time period but got to experience it later. While my first pre-crash experience was an Atari 2600, I really preferred the smoother graphics of the Atari 5200 and Atari 8-bit computer line. The XEGS released 2 years after the NES, took that already existing computer line and simplified it to make it seem more like a regular console. The controller was a bit better than the 5200's and there were more games that were not available on the 5200, such as Donkey Kong. I tried many of the other branded consoles but I didn't like any of the others quite as much as the Atari systems.
3rd Generation - NES:
I still didn't have my own gaming system till 1993, so the NES was my great budget system while growing up. So many classics and I was introduced to so many styles of games with this thing. I was lucky I didn't have to expereince any of the bad games during my childhood. My grandma was smart about buying good games only. I didn't get a SMS till years later and have been enjoying some of its games, but NES just has so much more that I am familiar with.
4th Generation - SNES:
My first game console was a Sega Genesis, but all I was ever interested in on that back then were the Sonic games and games featuring cartoon characters. SNES had more of those longer platformer games where you could save your level completion progress to the cart battery and re-play levels you already cleared. RPGs and adventures usually had better graphics and sound than the Genesis offerings of the genre. During this generation I was a kid so I liked the colorful games rather than the mature type fighting games or shooting games. Because of getting NES games cheap, I also had some go-to series I could ask for just because I liked their NES counterparts. While I didn't get any RPGs for it as a kid, Zelda still allowed me to experience some sword-wielding adventuring on it. The RPGs I tried in later years were great though.
5th Generation - Playstation:
My first jump into this generation was the Nintendo 64. I was all excited about the 3D and the exploration involved in games like Super Mario 64 and Goldeneye. But when my stepdad introduced me to his Playstation I enjoyed the great variety and quality games it provided. If I wanted any kind of game 2D or 3D, the Playstation had it. I was a preteen at this point and started to like fighting games and finally understood RPGs well enough to fall in love with the genre. It was also the first system I experienced that had demo discs. Those alone made the system enjoyable as I could really look forward to new games coming out, hoping my stepdad would buy them. When he gave his spare system to me it ended up getting the most play time from then on. It is still probably the system I play the most. Saturn is fun, but I've barely had the time to get into it yet.
6th Generation - Playstation 2:
Take everything that the Playstation offers and boost its graphics. So many more games and many genres to choose from than the competition. Being a teenager this had my first DVD player as well. Playing PS1 games on it was convenient at the time, making my old PS1 system only needed for Gameshark and eventually imports. I had a Dreamcast before PS2, but only really wanted that for Sonic Adventure. Gamecube I was mainly excited about because of Sonic seemingly finding a new home on Nintendo consoles (until he went multiplatform with Sonic Heroes), and the usual Nintendo characters games. I only wanted an Xbox for Oddworld: Munch's Oddysee, because one of my favorite Playstation series turned traitor and jumped ship. Playstation 2 ended up being the main system to get all the niche RPGs.
7th Generation - Playstation 3:
It took a while for this to catch up but with all the unplayed material from the previous generation, the backward compatibility of the first model came in handy for backing up my saves. No more worrying about corrupted memory cards! I actually originally bought the system for the convenience of infinite memory cards. Once the niche RPGs started to really favor the console as I had guessed they would due to the brand's previous consoles, I started buying more games for it than the other two. This was the generation that began when I had finished high school and started as an adult. With my disposable income I bought all three systems to try them out. Wii had its interesting Virtual Console to introduce me to TurboGrafx-16 and Neo Geo for the first time and its usual Nintendo characters+ exclusive Sonic games to get me to bite. I didn't really play it much until I modded it for roms. The Xbox 360 didn't really have anything that made me feel like I had to get it. It was more just a thing I purchased because I had the money to and have it just in case there's an exclusive I want. I do like Pac-Man Championship Edition from the Xbox Live compilation disc a lot though, and I scored an exclusive RPG Blue Dragon for $5. There's something to say about familiarity winning when it comes to consoles. The brand jump from SNES to Playstation isn't a big surprise when you compare the button layout of the game controllers.
2nd Generation of handhelds - Game Boy:
It may have been black and white but much like other Nintendo brand systems it had its established franchises to keep me playing it. The save battery useage was similar to that of the SNES games so when compared to Game Gear, the games just seemed longer and more enjoyable. My first Game Boy was the Game Boy pocket in 1997 while I didn't have a Game Gear till 2000. It took longer for me to get handhelds than consoles growing up for some reason.
3rd Generation of handhelds - Game Boy Color:
This one pretty much wins by default. Neo Geo Pocket Color was really good and had better fighting games than any other handheld before it, but there weren't as many games. Game Boy Color didn't even have very many exclusive Nintendo franchise games on it but the few it did have were great. Pokemon, Dragon Warrior and Zelda + a couple platformer remakes was all it needed. That and adding replay value to older games by adding color helped. I still liked my Super Game Boy better for those older games though.
4th Generation of handhelds - Game Boy Advance:
The stuff this thing was competing with really didn't have much recognition in the gaming community. In general, I would say this is the best Game Boy of the three generations of that line when it comes to the games themselves. It really was a leap forward from all handhelds that came before it.
5th Generation of handhelds - Nintendo DS:
I really like my PSP but I gave the Nintendo DS a slight edge for having such a huge library and a large supply of Nintendo franchises, exclusive Sonic games, and even RPGs like the Final Fantasy III, Dragon Quest IV, Dragon Quest V and Dragon Quest VI remakes. The PSP seems to have tons of the kinds of games I want though too, so I can see this opinion changing in the future. Closest thing I have to a draw in all of my list actually. The one thing DS has over PSP is longer battery life.
6th Generation of handhelds (so far) - 3DS:
For me right now, this is THE system to own this generation. Even if the consoles and PS Vita don't end up doing so well, this thing already has some really fun games on it.
So yeah pretty much my favorite 2 game companies over the years have been Nintendo and Sony. Sega came close at times, but that was a really long time ago.