I was raised in a poor family (we've only been able to afford gaming stuff when I was 13) so my choices are quite limited to a few systems. Though to be fair, it will be hard for me to decide which is/are my favourite games so I might end up listing a lot of them.
We had a gaming console when I was 5 or something around that age. I cannot remember how we acquired it nor can I remember what was it called and what games we had for it. I do remember playing a game with my dad on that console, so that game, whatever it was. :p
GBA: Final Fantasy IV, Final Fantasy V, Final Fantasy VI, Pokemon Emerald, Megaman Battle Network 6: Cybeast Gregar
These games were my "childhood." I say childhood, but I was well into my teens when I started playing these games so perhaps I should say "teenhood" instead? That sounds really weird though haha. It's hard for me to pick a favourite within these games because I still play all of them until now, albeit on an emulator because my GBA died a long time ago. Notable runner ups would be the other Advance-gen Pokemon games, Megaman Battle Network 6: Cybeast Falzar (sorry Falzar you're not as awesome as Gregar), Final Fantasy Tactics Advance, Fire Emblem: The Sacred Stones, those fake "100 in 1" packets, and Golden Sun.
PSP: Final Fantasy Tactics: War of The Lions
After my GBA broke, my dad bought me a PSP. I was still able to play GBA games on it thanks to the gPSP emulator, but most of my time was spent playing WoTL. I did so many things in that game including, but are not limited to, playing through the story many, many times, hacking the game to include unobtainable classes, grinding to get the Dark Knight class immediately after random battles are a thing. The original Tactics game on the PS1 was pretty amazing too (I've played it on an emulator) but it definitely can't beat everything I've done on the PSP version.
NDS: Pokemon White 2
To be fair, I got my NDS literally a month before I got my 3DS so the only game I legitimately owned there was White2, so it wins by default I guess :p
3DS: Bravely Default, Pokemon Omega Ruby
I got my 3DS more than a year ago to play Pokemon Y and I'm hoping to own more titles for this handheld. I have a small collection at the moment but I'm looking to expand it later on! As for the games, Bravely Default was amazing! Playing through it reminded me so much of how I enjoyed jRPGs, especially the classic final fantasy games. I have FE:A still on hold because I haven't had the time to figure it out yet, haha. Pokemon Omega Ruby is a favourite because it's a remake of Hoenn; my very first Pokemon game! The list will likely change if/when Square Enix decides to release some of the FF classics on the 3DS :p
Xbox One: Killer Instinct, Kinect Sports Rivals (lol), Just Dance 2015
I discovered a liking for fighting games thanks to Killer Instinct. I'm still a masssive scrub at it but at least I can make relatively long combos now 8D The other 2 are family friendly games that I've been enjoying with the family. It was 99% the reason of my inactivity during the holidays :p
PC: Minecraft, Civilization V, Team Fortress 2, Dota 2
Possibly many others but these are the games I always come back to every now and then so I guess they're technically my "true" favourites. Oh and...
Wow I kind of made a wall of text there, haha. Well this was a very nostalgic experience! I've played the other consoles via emulator so don't worry, I'm not missing out on everything, just some of them! :p