I realized that I haven't given much of an introduction to myself for readers of this blog, and since a "favorite games" list says a lot about a gamer, what better introduction than such a list?
Presented in no particular order.
Metroid (NES). This was the first game I really fell in love with. I had seen the commercials and read about it in a gaming mag or two, and the idea that you could explore a giant maze while fighting your way through it action-game style really appealed to me. In my first experience with it, I was relegated to "mapper" as my friend Richard, who had just gotten the game at my urging, played it through the night and into the morning. It wasn't until years later that I got my own copy, bought brand new near the end of the game's original (silver box) production run.
Mike Tyson's Punch-Out!! (NES). I fell in love with the arcade Punch-Out as a 10 year old, and pumped quarters into it just as fast as Bald Bull could lay me out. When I learned a version of the game for the NES came out, I wanted it. Badly. Mike Tyson's Punch-Out!! is the epitome of everything I love in a videogame. A perfectly designed difficulty curve, pattern recognition, an epic final "boss," and a small moveset that you had to use better, faster, and more fluidly in order to beat the game.
Goldeneye 007 (N64). I'm not an FPS fan by any means, but Goldeneye grabbed me. It had great control, a good challenge even on normal mode, and plain had a cool atmosphere. The thing that kept me coming back was the higher difficulty levels (which had new objectives) and the cheats ("Facility 00 agent in 2:05? Are you kidding me?" I had to do it. Had to).
Vagrant Story (Ps1). One of the few videogame stories I ever really got into. But that's just icing. RPGs are very hit or miss with me, and Vagrant Story was a hit. If you didn't invest in the combat system, the game became borderline impossible about midway through. If you did invest in it, it was still a stiff challenge. I loved the straight up dungeon crawl, with no open fields to fill content or sink time. Great level design and engaging combat, and one of the nicest looking PS1 games to boot.
R-Type series (Delta and R-Types), PS1. I'm a huge shooter fan, and often lament the death of the genre. The Playstation R-Type games were among my favorites, featuring crazy level design (Stage 7 of R-Type 1, anyone?) and requiring twitch reflexes on top of pattern learning. Even after you knew the enemy patterns, you were by no means guaranteed a free ride. A no-force, no item R-Type Delta run was my crowning achievement of this series. Hell, just finishing R-Type with unlimited continues gives you bragging rights. That's how tough they come.
MDK2 (Dreamcast). Great platforming, fast, challenging combat, and incredible boss fights (OMG, Zizzy with Max!), all topped off with a big dose of humor. Level 8-C, climbing the nuclear reactor, is one of my favorite levels of all time. Almost perfect difficulty balance (stage 9 was a little on the easy side, but hey), you were pushed to the limit surviving even in the early stages. I had hopes of a 3-D Metroid being like this. And please ignore the dumbed down Ps2 version.
Mars Matrix (Dreamcast). Although I love shooters, the more extreme of the "bullet hell" types emerged, the less I liked them. Mars Matrix has a nice balance of bullet barrages and maneuverability. I still haven't finished the game on three credits. I sunk hours into the Elite Modes, racking up scores that cracked every top 10 of the (now defunct) official Mars Matrix score tracking site.
Shinobi (Ps2). A contender for my favorite game. Great, old-school flavor platforming with a modern touch (wall running) paired with great combat and tough bosses. Shinobi has a perfect difficulty curve, culminating in one of the best(of not the best) final boss fights I've seen. And that's just normal mode. Games are all about the challenge, and Shinobi delivers in spades.
Devil May Cry 3 (Ps2). I really enjoyed the first DMC, and the third took that, polished it up, and dropped you right into the fray the second the game started. Normal mode hooked me, and the harder ones kept me returning. Nice, classic-style boss fights (both in challenge and pattern-based flavor) and the normal enemies weren't simply cannon-fodder filler. Outstanding, responsive controls really pulled everything together.