I do fly solo
Half-Life series & Portal: Obviously, this shouldn't surprise anyone as I've been making repeated references to Valve lately. Half-Life is hard as hell, and that's inspired me to practice it to make a no-death run. Going through the whole game without dying once is going to be a very difficult challenge, but I'll be very proud if I can do it. I don't care if you think I have no life, because this is my hobby.
Mega Man series: There's a reason they're making new games now in the old style. It's not simply because old-timers like me like the style, it's because you don't need anything else. Sales figures have shown that the community doesn't always care about games being theatrical masterpieces like Final Fantasy as long as things are reasonably clear as to what they are. Kids still like 2D cartoons as much as they like 3D. Good visual & audio presentation are definitely good tools, but if you're working for the tools instead of the tools working for you, you're doing something wrong (unless your career is that of developing tools). That little gripe expressed, Mega Man has generally carried great level design, good challenge, and great music. The story isn't exactly refined (moreso in the later series) precisely because it's a level people like. Most people don't care about the Mega Man storyline and are more fascinated navigating through the game.
Nintendo staples: Uh... yeah, pretty much every first-party game Nintendo releases is a masterpiece worthy of anyone's time. The Legend of Zelda, Super Mario, Metroid (kinda second-party there), Pokemon, these are all great entries I've enjoyed. All of them exercise a good level of innovation with each entry too, although the Legend of Zelda series is kinda the slacker among them, thriving more on familiarity.
Dr. Brain series: The best puzzle games you've never played, these old games by Sierra for the PC are very good at challenging your capability for solving puzzles. Their puzzles work on all areas of the brain, so I'm pretty sure you'll find challenge somewhere even if you're part of MENSA. The presentation got a little kiddy as of #3, the Lost Mind of Dr. Brain, but they definitely don't tone down the challenge.
Punch-Out: I think of this as an active puzzle game more than a fighter. It definitely has elements which would make you better at fighting games, because you have to see what attacks are coming and respond appropriately in time. By the time you're good enough to know their specific behavior, you've probably gotten good enough that you don't strictly need it.
Sonic 3 & Knuckles: If I feel like I want to get some speed going and just take a platformer really hyper, this is the way to do it. Sonic 3 + Sonic & Knuckles together makes for a fairly long-lasting game with plenty of good opportunities to get Super/Hyper Sonic and blaze through the levels.
Doom: Ok, it's not strictly single-player, but the challenge offered in that mode is rather intense. I've managed to beat 2 episodes on Nightmare, 3 on Ultra-Violent, all while getting down to basics for shooters. It really is something when you're trying to navigate through a bunch of fireballs flying at you. and dash through things that are trying to kill you. Definite adrenaline rush!
Leisure Suit Larry 6: This one's always good for a revisit if you find one particular one you like. For me, that's #6 with full voice acting. It's a point & click adventure game themed on comedy, starring a loser trying to score with all sorts of women way out of his league, resulting in hilarious failures. You can see how much my mother cared about exposing me to sexual humor when she allowed me to play it at age 12 (I was astoundingly oblivious to most of the jokes then).
If you haven't played any of these titles, I strongly suggest you do so. I've seen few people who didn't enjoy these games.