For me it's
US released game systems, whether console, handheld or computer
Cartridges of arcade ports for pre NES systems
Complete in box games for systems NES and on
Specific favorite genres to collect for:
RPGs
Adventures
Platformers
Arcade Ports
Fighters
Puzzles
And most of all, games that belong to favorite franchises like:
Mario
Sonic
Donkey Kong
Kirby
Zelda
Final Fantasy
Dragon Quest
Oddworld
Legacy of Kain
Bust-A-Move
Dragon Ball
X-Men (and to a lesser extent other Marvel characters)
Suikoden
Pokemon
And of course many many others. The list could go on and on all day.
I guess an easier way to say this with a broader term is that I collect games that are in my opinion fun, good ones.