The world at large as decreed it's soccer but I have my doubts. My own countrymen prefer (american) football. Baseball is my national past-time and it draws big crowds. Polo, Cricket, rugby and other strange "foreign" sports don't register on my radar at all so it's difficult to judge.
Personally, my vote goes for fencing, but it is admittedly not a spectator friendly event.
And one note regarding the little flame war between (american) football and world football (soccer). Soccer, by definition is not a contact sport because players are penalized by the game rules for intentional (and sometimes unintentional) contact; in this way it's similar to basketball. Yes, contact happens and often it's violent but that doesn't make it a contact. sport. American football and hockey are, by definition contact sports. Not only is contact allowed in by the rules (with exceptions in both) it's an expected, critical part of the game. This point doesn't make either sport "better" per se.
I suspect the reason for soccer's popularity is the simplicity of the game and equipment required to play. Football more or less requires substantial amounts of equipment or you risk regular, serious injury. Soccer requires only a ball and a few people to have something resembling a game. It's simply more accessable for the world at large.
Both sports are spectator friendly to a degree, but I personally don't really care for either. Soccer often seems to be similar in basic style to basketball, where unless there are wide differences in skill you watch a ball more back and forth on the pitch (or court) and for much of the game the two teams are fairly evenly matched. Soccer may indeed require tremedous skill but it often appears to be a match of sheer endurance, something that does not, in my view make for good television. That said, it appeals to so many people that I have to assume I'm in the minority.
Finally, we come to the subject of whining. Soccer does seem to generate a fair amount of unnecessary whining among the players, and often it seems to me that it is simply a show for the ref. A player will go down clutching a body part and the minute the ref passes judgement, either by doing nothing or giving a card the player hops up and continues on their way. Behavior like this is cheating at worst, unsportsman at best, but it's hardly native to soccer. Most cotact sports have very specific rules dictating what is and is not acceptable contact, and there is little good to be had trying to sway a referees opinion of facts on the matter. The only sport I partake in is fencing, and though you make frequent equipment to body contact it's not truly a contact sport. Body contact of any kind is prohibited by the rules. The sport also generates a great deal of unrealistic whining - yes, sometimes it DOES hurt but that's a part of any sport. When my opponent stops a bout every 3 - 4 points because I have injured thier arm/leg/hand I get annoyed because I'm quite certain they are fully capable of carrying on and they are simply trying to gain a moments respite to reevaluate their strategy.