Sticking strictly to consoles and ignoring handhelds and PCs (which I also game on):
NES
Genesis
TG16
SNES
PlayStation 1
N64
Dreamcast
PlayStation 2
XBox
GameCube
XBox 360
Wii
PlayStation 3
A few of the systems I ended up owning multiple versions of for various reasons, but didn't bother to list them. The NES was the first system my parents let us have. Previous to the NES I had to play games at my grandparent's house... they had an Atari 2600 and Colecovision for the grandkids to use. It may also be worth noting that the Xbox is modded and has emulators for many old game machines like the MSX 1, MSX 2, Sharp x68000, Amiga, Sega CD, NeoGeo, NeoGeo CD, Master System, etc, etc...