I feel like everyone has something to say about what to do with the fighter, however, I think this merits a new thread.
In my experience the fighter really develops most of his problems later in the game (after around 8-12th level).
1. Easily incapacitated by magic.
2. Low mobility.
3. ACs scale much more quickly than attack bonus.
4. Skill selection leaves much to be desired.
These merit additional discussion.
Fighter's only have one good save, fort, and unfortunately it doesn't usually help them avoid or escape magical incapacitation. A single well placed battlefield control spell can end a fighter's involvement in combat for the rest of his, now short, life. Solid Fog, Wall of Force, anything that forces a will or reflex save, blindness, etc., can all stop a fighter so effectively the player might as well not be at the table.
A fighter can't fly. Nor should he. However, something must be done about either the prevalence of flying foes (wizards, sorcs., clerics, bards, all manner of flying beasts) or a fighters poor ability to actually enter melee combat with his foes in the late game. Another difficulty is performing your full attack. Most of a fighters combat ability can only be brought to bear as a full-round action. If a fighter has to move every round to enter melee with a mobile foe he's basically useless.
Unless some odd rules combinations are coming into play a figher doesn't typically gain more than +1 or +2 to his net attack bonus each level (on averagy). So by 20th he should have something in the +40-+50 range (this doesn't scale evenly though, typically you can have a relatively high AB in the mid-levels but then see it increase much more slowly from 12-20). ACs happen to be easier to increase: magic armor is cheaper than magical weapons and spells granting AC are easier to come by then those granted long-term bonuses to attack (or different stackable types of bonuses).
A lesser issue is his lack of skill selection. In a few ways this can directly impact his combat ability. Why doesn't a fighter have Perception? Even a warrior has listen and spot. It seems to me that a person who's primary form of employment is guarding things, or attacking things guarded by people like him, should be proficient in detecting threats. However, that aside, a fighters lack of skill selection can make him just plain boring outside of combat. For players who play only for the gory, combat dominated games this is not an issue. I think most play more balanced campaigns though, and find this to be a major sticking point. Many fighters find they can take a snack/smoke/bathroom/beer break during non-combat periods and not even be missed?
The Solutions
PFRPG has taken some good steps towards making the fighter more attractive. However, I've always felt the method for "fixing" the fighter is already present in the feat system. It could be incredibly flexible and is simple to understand. I fell a series of short chains should be created, the earliest feat in the chain would provide a neglible to small benefit, with subsequent feats granting far larger benefits. This would decrease the ability of any other class to snag all the major benefits while allowing a fighter to put his many feats to use.
A few abilities that should be available come to mind.
1. Something that allows a fighter to shrug off mobility reducing magic (or other magic for that matter). A standard action that can be performed under all circumstances, requiring a fort save, or some other check, representing a fighter's ability to "walk it off."
2. A chain of feats that grants very high bonuses to attack at later levels, earlier levels would grant lower bonuses. Weapon Focus at 1st level is good, G. Weapon Focus at 8th is not, and past 8th level something like a +6 or even +8 would not be too much.
3. A chain of feats allowing a fighter to move and still take his full attack (in 3.5 pounce was king but maybe a short three feat chain could simulate its effects).
4. Increase a fighters trained skills and class skills. If done well this doesn't need to overpower a fighter, merely increase the enjoyment of figher players.
I realize there are currently alot of feats available but with few exceptions (Shock Trooper and Combat Brute from Complete Warrior to name a couple) they are mostly lackluster in the 12-20th range.
As a side note, PFRPG has significantly changed the Power Attack feat, removing what used to be the mainstay of most fighter's abilities to deal damage. I agree that Power Attack was generally too dominant in fighter characters but in my opinion that was not because it was too powerful. It was because the alternate options were much too weak.