Through most of my youth in the 80s and early 90s, arcades, platformers, and other action genres were my main staple. After I discovered RPGs through Dragon Quest, that genre also became a big part of my gaming experience.
I had seen some examples of the Adventure genre back in the 80s via DOS ports of 70s mainframe text adventures Advent and Zork, but I never got very far into them. Then there was the Maniac Mansion port for the NES that I also never could get through. In the early 90s, Someone brought a copy of Leisure Suit Larry into my high school computer lab, but I didn't get to spend more than a couple minutes tinkering around and probably never even made it into the bar. It wasn't until the mid 90s with Myst and King's Quest 6 (CD version) and the purchase of my first PC that I really dove into the genre, soon buying compilations of all the past Sierra quests. I also got into some of Sierra's then newer IPs, such as Gabriel Knight, which gave me inspiration for my user name.
I had played through pretty much all the Sierra library by the time the genre collapsed and the company pretty much folded by the end of the 90s (most LucasArts adventures didn't draw enough of my attention to spend money on them). A couple years later, I got back into console gaming with my first PS2 and eventually a Nintendo DS. Somehow I built up a huge backlog of games to play from multiple genres, and Adventure games have slipped back into a serious minority in that.
As for the games listed above, I've either already played most or haven't had enough interest to check out the others due to so many other games I want to play. But here's a few thoughts:
999 - oh man, I wish I had bought this for a relatively low retail price when I had the chance. But I didn't want to then as no one I knew had said anything about the game at the time. By the time I started hearing people rave on it more recently, it's now very hard to find a complete-in-box copy for a decent price. I'd also be interested in the (semi?)sequel Virtue's Last Reward, but I don't even have the system to play that on.
Phoenix Wright - looks interesting enough, but I never got around to seriously checking it out. At this point there's so many games to catch up on, my completionism wouldn't be satisfied until I played them all, and my backlog is bloated enough as it is :(
Lux-Pain - the poor man's 999. I seriously bought this thinking it would be a decent alternative to 999 once I heard how good that game was, but I'm afraid I'm being sorely disappointed. The concept seems solid enough, but the execution leaves a bit to be desired. On top of that, the translation is borderline terrible, even disagreeing on the game being set in Japan or the US depending on the captions or voice acting.
The Walking Dead - looks cool, but I have no way of playing it and am borderline tired of the zombie story genre at this point.
Indigo Prophecy - I may check that out, if I can find it for a reasonable price. I had no idea the PS2 even had pure adventure games (besides Myst series ports), heh.
Heavy Rain; Beyond: Two Souls - I probably would like these if I end up liking Indigo. From the previews I have seen of Beyond, it does look quite interesting, especially the facial capture tech they're using. See video below:
(note to eDay or Philly: we are missing the Media tag from the formatting hotbar... well, it's there under eBay, but that's not very intuitive)