How about instead of defining the fighter directly, let's define the stuff around him. Then see where the Venn diagram takes us (i.e. the center of all this stuff, with some overlap). For sake of argument, use what has been in the past across many versions, even if somewhat inconsistent and the new version might change some of these. I'm leaving out the mostly dedicated casters as too far afield to be useful:
Ranger - pretty good with axe, spear, and bow at a minimum, more weapons depending upon archetype, wood lore including tracking, possibly animal companions, more controversially--nature spells, certainly skilled in the wild, knows certain creature weaknesses.
Barbarian - some decent selection of weapons, probably culturally based, hits hard with big weapons + special abilities to go berserk, skilled in the wild though more mundane than the ranger, really tough, mobile.
Paladin - knightly weapons, mounted combat, often uses a shield but willing to pull out a 2-handed when smacking more important than not getting hit, heavy armor, laying on hands and related curing abilities, some supernatural way to deal with undead and/or demons, some clerical ability, personable, fairly tough.
Rogue - shifty and weaker than the fighter, but capable of putting out the hurt when circumstances are right (circumstances gradually improve across versions), lots of specialized skills, usually favors light weapons, sometimes social skills, sometimes minor ability to use restricted magic items, mobile.
There is a lot of overlap there already, before we even put the fighter in there. So let's start with the fighter being at least competent with all weapons and armor (and this meaning something), and see what else we can fit in the center. There is nothing shared by 3 or more of those. At least two have: Mobility, tough, wilderness skills. That last one is not something we won't to overlap, but let's be a bit more expansive. Three of them do have: Some serious skills and capabilities to put extra hurt out.
So my starting place is that fighters get weapons and armor, can move decently, some toughness, some good set of skills (perhaps picking a subset from a wide range, and should be able to either pick classes of monsters to be good against or perhaps better get some special abilities to smack that are good against any opponents. Let's top that off with easy access to mounted combat/riding, and some analog to the 4E abilties to actually protect friends.
But I'd be interested to see how that set might move, if someone wants to add other classes to the mix (monk? cavalier?) or add things I may have missed.