PS One would've been it for me, the memory is too hazy to remember exactly what games we got with it the day of but Crash, Spider-Man, and Spyro ended up being a huge part of what library I could muster as a single-digit child. We ended up with a few pieces of shovelware, but for the time it wasn't like I was able to be much of a discerning force. Action Bass was the only game I think I can firmly say everyone in the household, including my mom, were able to play and compete over.
Honorable mention would probably be the 360? I remember really wanting to finally experience online games and it was amazing my family was even able to foot the bill considering we were in a pretty bad situation financially when we got it, and getting my parents to finally relent and let me run an ethernet cable into my room let me experience something that would introduce me to my most important friends and my partner. For all the games we got bundled with I think I ended up spending the majority of the weekend playing Ultimate Mortal Kombat 3 off XBLA.
Both of my parents (divorced) made the collective decision to buy Wii's the same year, pretty late into console's lifespan without communicating with one another, and I always find that one funny to look back on too since they both felt like they were copied.