No single roleplaying game can cover all demands. No, not even that one; or at least not without spending oodles of money. Some systems are easier than others at being flexible, as long as the system itself is divorced from setting. Some are inextricably tied to the setting. The marvelous (and marvelously complex) Skyrealms of Jorune comes to mind, for instance or, to a lesser extent, Empire of the Petal Throne (both of which I love, incidentally).
More to the point, no single roleplaying game can cover all demands simply and with little modification. i believe that fantasy games that include a magic system are the big culprit here. Magic systems require an underlying philosophy or set of mechanisms that stray from the core thrust of what it means to roleplay. It is a beautiful appendage or is so tied in with setting that, like the two examples above, it is inextricable. And, well, it's magic, so it's supposed to be something out of the norm, something extraordinary. It doesn't behave by the same rules that govern "normal" human interaction (even if the "normal" interaction is thrusting a sword through a dragon).
When I want to introduce someone to roleplaying, and they want to play a fantasy game, I default to AD&D (a mixture of 1e and 2e) or, more commonly, Dungeon Crawl Classics. If they want to play a horror game, I use Call of Cthulhu (7e) or, more recently, Trail of Cthulhu/Casting the Runes, as these all have solid, fairly simple rules for sussing out information.
In all other cases, when I want to introduce someone to roleplaying and want to keep the emphasis on the roleplaying and not merely rolling dice (not that there's anything wrong with that, you roll how you roll), I like to use an unlikely contender: Traveller. Or a stripped down version of Traveller. Let me explain.
Traveller is often thought of as one of the original scifi RPGs, and this is true. Oftentimes the setting is conflated with the system in people's minds, but the setting came after the fact of the game itself. Yes, the Imperium is a rich setting that I recommend quite strongly, as the abundant resources allow you to enter a rich universe and explore it with your players. However, the game came first, the setting second. To quote creator Marc Miller from the interview linked above:
"I envisioned a generic rules set that would enable any science-fiction situation, from space opera to serious drama. One of the first reviews of the game said something like 'I won't play a roleplaying game that doesn't provide background and adventures,' and the editor interjected, 'And I won't play a game that constrains me like that.'
"I'll confess that was an awakening for me, and I realized I couldn't make this game all things to all players; I had to choose. Our reasoned corporate choice was to provide background and adventures for those who lacked the spare time to make up their own."
I would argue that Miller's first sentence is an understatement. While I don't think one can safely scratch out the words "science-fiction" from his response, one could feasibly do so, if one adds the word "almost" in front of the word "any" (his bold, not mine). Again, magic is problematic, so if anyone wants to take the time to concoct a workable magic system on the skeleton of Traveller, I am all ears. I don't have enough lifetime left to do so, with all the other RPG projects I'm currently working on and have lined up for the future. So, have at it!
Barring magic, I believe that the skeleton of Classic Traveller can bear the muscle of just about any genre or setting you'd like to tackle.
Classic Traveller has been lambasted for the fact that one's character can die before even entering play. A valid concern (that I don't share, but that's a different story). So . . . skip that whole process altogether. Simple. Here's how:
First off, you need to roll your character's stats. They are, in order:
Roll 2d6 for each, in order. If you are into hexadecimal notation, you can shrink just about everything you need to know about your character into one line of hexadecimal code. Numbers 1-9 are just that, the numbers 1-9. The number 10 is represented by the letter A, 11 is represented by B, etc. So, for a character with STR 10, DEX 8, END 6, INT 11, EDU 9, and SOC 7, you would have:
Easy peasy. You have everything you need to play.
No, seriously, that's it.
How do you determine if a task is "doable" by your character? First, pick the stat that you think is relevant to the task. Justify this to your referee. "I'm looking for hidden clues. Since we're in a library, I'd like to use my Education," or "I'm trying to hold on to this cliff. I could use Strength or Endurance, but my Strength is higher, so I'll use that." Fine. Second, the referee should determine if there are any modifiers. They will add to your ability score if conditions are favorable, and subtract from your ability score if conditions are unfavorable. Third, roll 2d6. If you roll under, you succeed.
Of course, in our modern age of specialization, you will say "but my character is a doctor, shouldn't she have medical skills?" Of course. This is where skills come in. Determine ahead of time (or, better yet, on the fly, if your referee is cool with it - I would be!) a skill you might have, given your training, background, etc. WARNING: This is where things get touchy, statistically speaking. I would strongly recommend having very few skills, as these represent a high degree of specialization and because you don't want to be a slave to your character's background. They're here to grow and change and become better, right? So, keep those skill levels very low. A "1" shows specialization. A "2" is extremely exceptional. A "3" is almost unheard of, near godlike. Be careful you don't skew your game into ridiculousness, unless you're trying to emulate Toon (again, if anyone would like to shoehorn Toon into Traveller mechanics, I'd be delighted to see and play this)!
Now, when you make your 2d6 roll for success or failure, you simply add the skill level to the chosen character attribute to determine your "roll under". For example, let's say our character above is a doctor with medical skill who is trying to resuscitate a companion who has stopped breathing. She uses INT (at an 11) + a medical skill of 1, so she needs to roll 12 or under on 2d6. Practically guaranteed success. Hopefully this also illustrates how ridiculously unbalanced the game might become with even a skill level of 2. Again, be careful (or dare to be stupid)!
One potential twist was introduced to me (and others) by Marc Miller when we played in a two-hour session of Traveller that he refereed at Garycon a few years ago. Yes, I was star-struck and a bit giddy. But I remember it well because it was so quick and clean. We rolled our stats, I asked about skills and he said "sure, you're all Imperial marines, so you'll have a skill of Rifle-1," and that was it. We were playing in about three minutes. Now, the twist: since this was a two hour session, and to avoid repetition, he had us rotate the stats we used. Once we used a stat in that session, we couldn't use it again. If you did a strength-based check, that was it, the rest of your checks that game had to use something other than strength. This was a neat way of limiting any one character who was overly-powerful in a particular area and spread the spotlight time to everyone at the table (there were eight of us playing). In a campaign, if you wanted to use this caveat, you could reset the board, so to speak, with each session. It's not necessary to successfully use the Traveller skeleton, but it does make things a little more . . . democratic?
He recaps what happened better than I can in an interview done not long after this session at which I played: