Two of the most entertaining and challenging games I have ever played would be Dark Souls and Demon Souls. Now a days, you can simply look up the optimal gameplay path on any FAQ website and really eliminate any real legitimate challenge. If you ever want any real satisfaction from a game, I would recommend trying to play without looking to a guide for help (as much as possible.) Some other fantastic games I have played first run-through without a guide, thoroughly enjoyed, and would definitely recommend to anyone are Legend of Zelda: Ocarina of Time(N64), Final Fantasy VII (Playstation), Final Fantasy X (PS2), Kings Field (playstation), Dark Souls & Demon Souls (PS3), ChronoTrigger (Playstation), Arc the Lad (playstation) and sequel for PS2, and Shenmue for Dreamcast, amongst many.
I will say again, I really think the challenge and enjoyment really come from personal stimulation in the fashion that you try to play through on your own intuition, seeking help when you've exhausted all your resources and ultimately limiting those times you go beyond the game to seek answers. One way you can challenge yourself is to play a game and tell yourself you can only look at the guide two or three times, like life lines, so that you use them wisely and challenge yourself to play through the areas that you couldnt figure out before.
Just my thoughts,
Edit for online games portion:
For online/multiplayer games I really enjoyed and were challenged by games like StarCraft Broodwar and Starcraft 2(melee) as well as some of the very complex User Map Settings (UMS) that people dreamed up like Legends, Evolves, Golems, PTQ (protect the Queen), DOTA (WC3,SC,SC2), BattleCraft, Squad TD, etc, you'll find that some were more or less unbalanced at some points and made it very challenging, and others that were fairly balanced and had a good following to seek some legitimate competition in. Furthermore, in Starcraft 2
Onto non PC games for me and some of the very earliest on-line console gaming I really enjoyed were Phantasy Star Online (Episodes and Versions 1&2 for DreamCast) and Alien Front Online (which was a badass online tank battle game) - interestingly enough, that is the first console game I had ever seen with real time voice chat. Socom 1 was Absolutely BAD ASS, Battlefield has always held my attention because unlike the mindless FPS that goes on in Call of Duty - at least in my opinion - There is SO much dynamic action happening at any time and anywhere. Aerial fights, tank fights, ground vehicle fights, infantry fights, It just goes on Battlefield 3 is my favorite FPS of all time, and I cannot wait for BattleField 4, 64 player warfare might just force me to tell my girlfriend and son I'm going on a 2 week vacation in the basement when it launches and I'll creep up from the depths into sunlight after I've gotten my fix.
There are other classics on here that I'm sure other people are very familiar with, again, depending on individual preference to tackling challenges. Self Found HC Diablo 2 is still something my friends and I communicate to one another about on a regular basis and log on and play to this day. That game will always be timeless to me. Aside from the obvious Diablo gameplay, I would also recommend Dark Souls and Demon Souls online gameplay because its complex in a sense that it takes a little experimentation to figure out what you can and cant do, as well as the boundaries of the in game universe. It's truly a gaming masterpiece, at least to me. I could type for days on this, but my girlfriend needs to use my computer's powerpoint
Dark Souls isn't that difficult once you know what you are doing, some frustrating bosses but not hard hard.
Ghost n Goblins, that Prinny game (dood), old inferno in diablo 3, Viewtiful Joe on hardest difficulty, Ikaruga, Sonic 2 (game gear / master system) Mario lost levels... Ah! I almost forgot, FUCKING DEATHWING SPINE HC and Parappa the rapper.
Edit: Dark Souls is a great great game and I love it. I can't wait for DS 2