The games I own "legit" copies of:
THPS1 (PS1)
THPS4 (PS2)
THUG1 (GCN)
THUG2 (GCN)
THAW (Xbox)
The games I used to own, but lost:
DESA (PS2)
We started out as only having THPS1, THUG2, and DESA. When we were kids, I would often watch my brother play them, and occasionally, I would join in and try (emphasis on "try") to play with him. I was terrible. But I was always fascinated by skateboarding, from everything I saw in the games, on the TV, and in the movies. THUG2 and DESA were the ones we played most; I even remember my bro making a clubhouse level in THUG2 for him and his friends to play around in (sadly, he took off with the memory card that had it, so I can't show any pictures or videos of the clubhouse in question)
Many years later, I ended up taking the GameCube and all of its games into my bedroom. (To this very day, I still treat it as if it were my child) A couple years ago, I bought myself THUG1 and THPS4, while receiving THAW through a game lot, and then I decided to finally start THUG1, THUG2, and THAW on my own. I fell in love with the stories of THUG1 and THAW, and loved just playing the games in general, and trying to find every single gap, tape, easter egg, and unlockable I could.
My favorite of the series? Definitely THUG1. While it may not have a vast amount of features like THUG2 does, I still think THUG1 is the high point of the series, not just because its engine feels better (aside from the on-foot physics), but also because it's the most accurate, down-to-earth depiction of the ups and downs that skaters go through when trying to start a career.