Which combat feats actually let you do something interesting?

[Tvtyrant]

The same as the title. Which feats grant you new actions or effects which are interesting or varied, as opposed to just adding numbers?

[OldTrees1]

Combat Reflexes gives you more attacks of opportunity. While this is a numerical increase it also opens up qualitatively different options you could not do before since you had too few AoOs per round.

Evasive Reflexes lets you move instead of making an AoO.

Improved Trip gives you a free action upon successful completion of another action. This is an action multiplier. While multipliers are inherently numerical increases, this yet again opens you up to qualitatively different options.

Knockback lets you bullrush without following, is yet another action multiplier, and cuts the action cost down from a Standard Action down to any melee attack.

Shock Trooper allows you to bullrush(or knockback) in curved lines.

There are several action denial feats. These impose a condition (Daze, Nausea, Staggered, Cowered) on the target that either cuts down or eliminates their ability to act for a period of time.
Boomerang Daze, or Dire Flail Strike
Three Mountains
Staggering Strike
Imperious Command

Similar to both action denial and action multipliers, there is some feat that allows you a free grapple on a successful attack.

Of course we should not forget mobility feats that add flight or teleportation
Dragon Wings -> Improved Dragon Wings
Aberrant Blood -> Starspawn
Shape Soulmeld has both options but its flight is weaker than the above feat pairs.

Increased reach is a numerical bonus, but there is a qualitative difference if you have 5ft more reach than your enemies. There is also a qualitative difference if you have 10ft reach(you now have interior and border threatened squares)
Aberrant Blood -> Inhuman Reach
Willing Deformity -> Deformity(Tall)

Edit: There are also way too many feats that give qualitative differences that are not worth a feat slot. I ignored all of those. (But this list is missing a few good combat feats that I can't think of right now)

[Dread_Head]

Martial study and martial stance give access to manoeuvres and stances respectively most of which do something interesting and varied. Shape Soulmeld, Bind Vestige and (Planar) Touchstone aren't martial feats but they all open up options for things to do in combat. Devotion feats from complete champion similarly give new interesting things to do, animal devotion for example can give a fly speed.

[OldTrees1]

Martial study and martial stance give access to manoeuvres and stances respectively most of which do something interesting and varied. Shape Soulmeld, Bind Vestige and (Planar) Touchstone aren't martial feats but they all open up options for things to do in combat. Devotion feats from complete champion similarly give new interesting things to do, animal devotion for example can give a fly speed.

Agreed

Note: Martial Study and Martial Stance are drastically inferior to 1-2 level dips in the base classes of the same book.

[Tvtyrant]

Agreed

Note: Martial Study and Martial Stance are drastically inferior to 1-2 level dips in the base classes of the same book.

Also arguably more expensive, since you get more levels than feats. Unless you are a caster and would lose spells.

[Flickerdart]

Knockdown is an excellent feat that essentially doubles your attacks (provided you spread the love to many enemies), since you get a free trip which triggers Improved Trip's extra attack. You can use that extra attack to do whatever it is you like to do with attack actions such as Disarm or Sunder.

[StreamOfTheSky]

OldTrees1 has a good list.

To add to it:
Combat Panache and Elusive Target both give fun re-directs of attacks, and some other stuff (Panache an attack penalty debuff and playing dead; Elusive lets you make power attack worthless and gives free trip attacks that don't even consume AoOs in a quantity directly proportional to the stupidy of the enemies).

Riposte (dragon mag), Karmic Strike, and Robliar's Gambit all give you decent counter attack abilities.

Backstab (dragon mag) makes enemies you flank provoke whenever they attack someone other than you, making it amazing on a tank paired with a rogue (or to turn the rogue into the most extreme glass canon ever).

Cutpurse (dragon mag) lets you pickpocket an enemy with Sleight of Hand while in combat. It's niche (kill the person and you can take their stuff anyway), but in games where enemies often escape it has its place. Also useful if you end up in a fight but don't want to kill the person (or they're way over your level and it's suicide to try), you can steal the MacGuffin and flee and let them think they "beat you." The feat lets you disguise its use as a combat maneuver, so they may not notice till long after that the item is missing.

Daunting Presence is a solid ranged debuff for any martial character to add to his repertoire with a pretty long duration.

Great Throw (Oriental Adventures) is sort of like a Setting Sun throw you can use as much as you want. You trip and throw them into any space you threaten (so it can be amazing w/ lots of reach; the trip has to be unarmed-based, but by RAW you can use your whip or spiked chain to determine the destination space) and they take your unarmed damage.

At Home in the Deep (Drow of the Underdark) is basically a Devil's See in Darkness ability. Lets you see through magical darkness, though only of the Darkness spell...

Mad Foam Rager lets you once per rage delay becoming affected by an attack/spell/ability for 1 round. Intimidating Rage, when combined with Instantaneous Rage or the Ferocity rage variant and the aforementioned Imperious Command, lets you immediate action cower-lock a foe within 30 ft for 1 round, completely disrupting their turn/action. Of course, the Never Outnumbered skill trick lets you also cower-lock every foe within 10 ft of you simultaneously.

[Deadasadoor]

I haven't seen it specifically mentioned, so Stormguard Warrior (ToB). While there are lots of ways to get more AoOs, it actually gives you something more to do with them. It also gives a good way to pierce DR/-.