My dad completely and totally surprised me with the OG Xbox a couple years after release. I felt like the luckiest kid ever already owning a GCN and PS2, but yay for Christmas, lol.
Anyhoo, got Ghost Recon Island Thunder and had a good bit of fun with it. Of course, got Halo a few months later when I had the funds.
A friend, totally randomly, bought me the most expensive gift a friend ever got for me back then - a $50 copy of some new Star Wars game I hadn't heard of: Knight of the Old Republic.
I was blown away. Upon finishing, it became my #1 favorite game of all time; and it hasn't been dethroned since.