I've seen a lot at my gaming club. I'm going to answer this two ways.
First, the way you asked it. I've seen all of these, both as pure fighters and as multiclass that includes fighter. Heavy weapon and archer have been the most common, almost always around feats.
Oh #2 and #5 do overlap a good deal in play - a agile sword and board fighter with dueling fighting style. They are definitely defense oriented, but not "tank" oriented, which may be what you were going for with #5.
Second, I'll flip it, with what I see the most of:
1) an archer fighter, focusing on ranged combat
Fighter, UA Ranger, and the occasional rogue. Almost always with one or both of Sharpshoot and Crossbow Expert feats.
2) an agile/mobile fighter, with dueling or two-weapon fighting
Rogue, Fighter, UA ranger.
3) a heavy weapon fighter focusing on dealing the most damage
Barbarian, Paladin (Vengence), Fighter. Exclusively with GWM. And while any of these can be X + Fighter multiclass, this seems to have a lot of 3 level dips into Fighter (Champion). Especially those half-orc barbarians with a d12 weapon, looking to crit that occurs 19-20 (champion) with advantage (barb) and does 3d12 (half orc racial).
4) a reach/polearm fighter, using pikes, glaives etc.
Paladin, Fighter, occasional Barb.
5) a classic "sword & board" fighter, focusing on armor and defense
Paladin, Fighter, occasional Barb