Soccer - the original game of footbal. Round ball. No hands (except for goal-keeper and throw-ins), lots of kicking. Very entertaining when skilled teams play.
Australian Football League (AFL) Aussie rules football. Oval ball. Lots of hands and lots of kicking. Originally from Victoria, now has interstate teams in the competition. I like it because it is moving all the time, is free-flowing and easy to follow.
National Rugby League (NRL) a variant of rugby. Oval ball. Lots of hands and very little kicking (but they still call it football). Native to NSW, but also incorporating interstate membership lately. Lots of stop-start, but there's usually something happening.
Australian Rugby Union (ARU) an original variant of rugby. Oval ball. Lots of hands and a fair bit of kicking (Believe an NRL follower once said there was too much kicking. Well, they do call it football, don't they?). More popular in other countries than rugby league.
Gaelic Football and International Rules football Don't know the full ins and outs, but is similar to Australian Rules. A round ball is used and a cross-bar between the goal posts defines a third scoring zone: "goals", "overs" and "behinds". Haven't seen many played, but it's enjoyable.
and then there's
American football: Grid Iron. Oval ball, throwing, running and a bit of kicking. Very orchestrated moves. Very stop start. Can have different teams for 'offensive' plays and 'defensive' plays - the change of possession being one of several reasons for play to stop and a conference to be had before the next play. A team gets 4 chances (downs) to advance a total of (at least) 10 yards. If they succeed, the counter resets and they can try to keep going. I won't offer any further comment as I'm sure an offended supporter would quite happily send a cruise missile my way if they could.
Anything else?