Wow. Interesting question.
By way of an answer, allow me to tell you the tale of Nelson, and the Gift of Champions.
When I was in Junior High (what you youngster now call 'Middle School'), and High School, there was a bit of a rivalry between Villains & Vigilantes players and Champions players. It was a very Marvel vs. DC sort of thing. Oddly enough, when Marvel and DC put out games of their own, Marvel went with random character generation (V&V), while DC went with point buy (Champions).*
I was a die-hard V&V guy for years, and so was my friend Nelson M. Nelson eventually migrated to Heroes Unlimited by Palladium Games, but his heart remained in the V&V camp.
In High School I joined in with William Corpening's Champions campaign, which I've discussed on the blog many times. I was totally hooked, and by the third year of the campaign I wanted a copy of Champions for myself. I wouldn't end up getting my own until the fourth edition hardcover came out, the 'Big Blue Book' as they call it. I was in love.
Nelson all but labelled me a traitor. He refused to look at Champions, soured on it as he was from years earlier. The thing was, I'd know Nelson a while by then. We were really close. So, I bought him a copy of the hardcover - which may I remind you was the most expensive single RPG book product at the time. It was about $35 dollars, while D&D hardcovers were maybe $20 tops. It was also monstrously thick, about that of the first edition, AD&D Player's Handbook, Dungeon Master's Guide, and Monster Manuals combined.
Now again, I knew Nelson. I knew that if he received it as a gift he would obligated to read it. It's just a quirk of his nature. A good one I might add.
In the end, he became a fan himself, and ended up running one of the coolest Super Speedsters I've ever seen in a Champions campaign I GMed sometime in the early-to-mid 90s.
I guess the point I wish to make with this tale is, there isn't any one game I would give to just any person. I would give Nelson Champions. I would give my ex-wife D&D, or Ars Magica. I am hoping to give the Tutoring Center she owns a copy of No Thank You Evil! when it comes out.
The right game, for the right person.
That's what it's all about.
*I always found it funny that although Marvel was like V&V, and DC (the Mayfair Games version) was like Champions, I was a DC Heroes fan in spite of being a V&V fan.