What does Euler's Identity have to do with that you ask? Good question, I think mainly it just means I studied physics and so I think its awesome. You may like it for different reasons.
Hows and Whys
Game systems all are meant to do something. Whether they do what they intend or not, they at least have a purpose behind them and some kind of theory that led the designer to use them. That theoretical underpinning could be as simple as "We made up some shit we thought would be fun." But even when there is no conscious decision, there is something there that tells us something about the designer.
My own theory of gamecraft is that games have two basic parts: story & substance. This is not an uncommon way to look at them and it can be explained with a popular saying: system matters. For a game to work out, the rules need to inform the setting and the setting needs to inform the rules. Plenty of games have broken this maxim and to me it is always to their detriment.
When the system reinforces the setting's assumptions though things really sing for me. For instance. AGON does this for competitive, Hellenic heroes seeking glory and fortune and weathering the whims of capricious gods. Legends of the Wulin does a fantastic job of hooking the setting into the system in a way that each reinforces the other as well.
I tend to think of systems as either specific or generic. It's fairly black and white for me, there's really nothing in the middle as far as I can tell.
The poster child of generic systems is GURPS. It's a good, solid set of rules, but I've never enjoyed using it. It simply doesn't speak to me because it isn't purpose built to do anything in particular. BRP is similar in that its purpose is to be as general as it can be and I do play it occasionally but it's never my first choice. Despite being a very close relative of BRP, Pendragon is one of my favorite systems because it has cut and modified its parent system to do one thing well. There are better medieval combat systems out there, but there is nothing better for emulating Malory.
I can't think of a single, iconic setting that I would hold up as an example of a specific setting. By their very nature there is no one way to do it, but I can mention a few that I really like.
Dogs in the Vineyard: It's about being a Mormon gunslinger charged with keeping order in the land. It's about making choices and what you are willing to pay for them.
AGON: Mentioned above. Greek heroes doing daring things and then meeting their fates. It focuses around a competitive aspect and it matters not only that the heroes succeed or fail, but which of them stands above the others during each deed.
Grunt: US soldiers in Vietnam. It's amazing. The paranoia and the psychological toll it takes on your boys are almost palpable around the table. It's Platoon, the RPG. I've used it for 40k Imperial Guard and it gives you a much different game than Only War to say the least.