Fate (specifically the most-recent incarnation: Fate Core)
I've been in multiple large-party scenarios with this system, for everything ranging from 8-10 person one-off convention games, to running a 9 month campaign with a rotating cast of 5-9 players (out of 12 different players who joined us at various points in the campaign), and this has been, by far, the easiest system I've ever played with a large number of players.
As others have done, let's look at your hit list:
Is pen and paper/tabletop, and does not require large amounts of space
Physical requirements are pen/pencil, paper, and 4 dice (Fate/Fudge dice or d6s will work in a pinch). A couple of small dollar-store whiteboards are nice for tracking temporary things like Zones (aka maps), and I keep a stack of index cards on hand for Aspects (you might have as many as a dozen for a full encounter, but rarely more), so something the size of a typical card table is more than enough for all of the system components, while the party can relax in whatever chair is handy (as long as they have somewhere to roll dice, we ended up using flat-bottomed bowls).
Is in a fantasy setting, or has no specific setting.
Fate Core is, by definition, setting-less. It is designed similar to Basic Roleplaying, d20, Savage Worlds, and other agnostic systems to specifically support any setting required, but there's tons of great supporting ideas and capabilities for Fantasy setting elements. Some of my favorites include the highly flexible options regarding magic spells, and the ability to portray detailed information about magic items simply by building them a character sheet of their own.
Has a character creation time of LESS than five minutes
This is one where there might be arguments. To me, Fate characters are extremely easy to build since they resolve around expressing an idea and a brief back story. A "Well-Trained Fire Caster" with "Anger Management Issues" who was "Rescued From An Orphanage" by a "Wise But Poor Family" is an entire character in one sentence. Skills to match would take a couple of seconds looking through the list, and using Fate Core's recommended skill pyramid makes it simple to even decide how powerful each is going to be. Things could be more complex if needed, but even then adding things like Extras (specific or unique abilities, substitutions, or exceptions to the rule) are still fairly simple to accomplish in a short time period.
Has a "low-crunch" combat system with a minimal choice of options available to players.
Fate Core's encounter system boils down to each player chooses an action they wish to perform from a list of 4 (some argue 5, but really, it's just 4), pick the skill they wish to use to perform the action, roll the dice and add their skill modifier (even at +0 skill modifier, so there's no difficulty with arguing over whether or not the "House-servant To A Highborn Noble" can help build a fortified defensive position... he'll just suck at it), and find out what happened from the GM (or frequently the rules give a simple "You usually need a 3+ for this" instruction).
For example, if the Barbarian says "I want to swing my Great Axe at the Goblin Warshield", he's just stated everything needed to figure out his action: he's making an "Attack" action using his "Fight" skill (melee), so he needs to roll dice and add his bonus, where his target number is the GM's roll plus the Warshield's defense skill (also "Fight" in this case).
Each individual's turn should only take 15-45 seconds, about the same as a board game.
Fate excels at this due to its narrative nature. Players describe what they want to do (possibly even helping figure out the mechanics needed as they learn a bit about the system), dice are rolled, and an outcome is determined. No charts to check, no criticals to confirm, no follow-up damage rolls. The only time we typically had discussions of any length is trying to determine how long certain actions would take (Summoning an Earth Elemental is no easy task!), but when we realized some actions like that might need time, we worked outside of the encounter (and sometimes outside of the game session) to determine certain 'pre-planned' actions and the time they would take ("Rocky" was a good friend, not to mention a great listener... just not that good at playing 'catch').
Is not -entirely- combat-oriented.
Another excellent part about Fate is that 'combat' and 'social interactions' are viewed as nearly identical, just affecting different parts of the target with different weapons. A thuggish rogue may wield a scimitar from the shadows with surgeon-like accuracy to slay his way through an alley full of guards, but a suave rogue may wield witty remarks, dashing good looks, and favors (real or forged) from the nobility to gain passage beyond those same guards without a single drop of blood shed.
Has no, or very few, conditions to track.
A physical damage track of 3-5 points, a social damage track much the same (both of which reset at the end of an encounter, so no need to keep up with them from one encounter to the next), and a set of possible long-term Consequences that you could count on one hand (or less, usually) are all that you need to worry about with Fate.
One other important factor I'll add for consideration: Low or no cost
Fate Core (and a lot of add-on material) is currently available as a pay-what-you-want system from the publisher as a PDF, or rather inexpensively for a hard-bound book. Very few publishers will offer an option like this, and cost can be an important barrier-to-entry for a lot of GMs and players. I've seen many great systems I'd love to play around with, but $60+ for a single book, or $99 for the "set of three" intro pack can get expensive after a while. Even the dice allow for some of the cheapest options with just using 4 common six-sided dice, instead of requiring a 7-dice set or even custom dice that aren't reusable for any other system (coughWHFRPcough).
Downsides and Disadvantages
I wouldn't be doing the system justice if I didn't mention a few of the potential downsides to Fate & Fate Core.
The largest of these I've encountered is the "D&D Generation Factor": some RPG players used to systems like D&D 3/3.5/4E/etc might have difficulty with a system as abstract and narrative as Fate. There's tons of discussion around here on game theory and Gameist versus Simulationist versus Narrative systems, so I won't go into the details here, but Fate favors lively descriptions of fantastical actions over page-turning to determine if the rules allow X feat to interact with Y item and Z class feature to deal infinite damage if they fail their fortitude save. The best way I've found to counter this is to forbid rule-books for the first two or three sessions, so they have to interact with the group and the GM to determine what they want to do and how to do it, instead of trying to find some loophole in the rules to power-game their way through. This may be something that can be very difficult to overcome with some players, so your millage may vary.
Another issue I've faced is players who prefer a Boolean "Success or Failure" result to their dice roll, and the fact that this really isn't how Fate was designed to work. For some players, they prefer having a fixed target number so they can focus their character development around reaching that number with every dice roll (examples include "Min/Maxing" a To-Hit bonus, or D&D 3/3.5's crazy huge crit range possibilities). A Fate GM will declare a target number for a skill check (or roll an opposed number), but after dice are rolled it's entirely possible for the dice-plus-modifier total to be less than the target number, but as a GM you can offer success... at a price (the hit might not do as much damage, the attacker might end up out of position or trip on his own feet, the door might be unlocked but everyone on the other side knows they're coming, etc). Fate/Fudge dice offer a statistical model that is much more of a bell-curve than the flat line of most other systems, and some players might not like this. Unfortunately my experience with trying alternatives requires messing with that bell-curve, and Fate mechanics tend to lose some of their effectiveness when you lose that curve, so I can't really offer any good alternatives from my experience.
I've played one-off games in probably 25+ systems, played 6-month or more campaigns in over a dozen systems, and I personally own more than 30 RPG systems (if you include variations-on-a-system like different implementations of d20, that number explodes), and ever since I've started playing Fate and Fate Core, I've been loving it above all other systems for both its simplicity and depth. While it's not the one-and-only system for all situations, it's certainly an excellent option worthy of a good look.