Growing up I had a Spectrum, CPC 464, Master System, Mega Drive, PS1, Dreamcast, and PS2, all as hand-me-downs from other family members (from PS1 onwards my parents stopped hearing "you've got kids, have this toy we don't use anymore" and started hearing "your kid seems unusually interested in these things, have this toy we don't use anymore").
After that, got an Xbox as a Christmas present, saved up and bought a 360 with my own money, bought a Wii as a present for my dad (and also for myself), and eventually a Wii U and an Xbox One. I'll almost definitely add a PS4 to that collection before Shenmue III's release...
As for what I still have, everything I didn't buy myself is gone; however, I have since bought my own PS1 and Dreamcast. I didn't particularly enjoy anything on the PS2 (when I had it, its main use was playing PS1 games), and the rest I can emulate easily.
Games I remember:
Spectrum - I had mostly compilation tapes, but Jetpac was always a favourite, as was Lazerwheel and Tintin on the Moon. Ant Attack is one I liked a little back then but like more now, and I wasted my life on Destructo but it was worth it.
CPC 464 - I loved One Man and His Droid although I didn't really understand it at the time. I understand it now and... don't really like it now. I also had a Spitfire game that I really loved, but can't seem to find now, as typing in "Spitfire Amstrad" gives me a completely different game - the one I remember had a side-on perspective more akin to Defender.
Master System - Sonic and Alex Kidd were definitely my go-to games; I'd completed Sonic 1, Sonic 2, Alex Kidd in Miracle World, and Alex Kidd in Shinobi World by the age of 7.
Mega Drive - more Sonic, but we mostly had beat-'em-ups that my brother used to piss me off by "accidentally" hitting me 36 times in a row and killing me.
PS1 - we mostly had driving/racing games for this, like Driver, Gran Turismo, Micro Machines, Rollcage, and Road Rash; I recall Fighting Force, the original GTA, Machine Hunter, Nuclear Strike, and Theme Park among them too.
Dreamcast - this was and always has been my "Shenmue and occasionally ChuChu Rocket" machine. Sure I had other games, but they didn't see much attention.
PS2 - Burnout, GTA3, and Stuntman, and the PS1 library. Two of those games made the jump to Xbox.
Xbox - Halo, SEGA GT 2002/JSRF, BLiNX, Kung Fu Chaos, Quantum Redshift, Need for Speed Underground, OutRun 2, Prince of Persia Sands of Time, and Burnout and GTA3.
Beyond that I bought my own games so there are too many to name and my favourites are already in the other thread.