I don't have one favorite feat, because no feat stands out as 'cool' to me on its role playing merits alone. But, I do have a short list of must have adventuring feats.
1) Improved Initiative: Simply put, a 20% extra chance of not being flat footed (and leaving your opponent flat footed instead) is hard to beat. Flat footed leaves you hugely vunerable to touch attacks, sneak attacks, power attacks, and a wide variety of other nastiness. Beyond that, it may be a truism, but I find it to be true more often than not especially at high level: "D&D combat is won by the spell casters, and often as not on the first round." There are very few combats that are going to go on meaningfully for more than 4 or 5 rounds and Improved Initiative means essentially that in this first few rounds you are going to have one more attack (or full attack) than your opponent. In the second round you've gone twice (maybe even three times if you surprised) compared to your opponents one time. That is huge.
2) Combat Reflexes: This is one of those feats with a double advantage, and any feat that gives you two worthwhile advantages is big. First, you can make attacks of oppurtunity while flat footed. This is hugely important for protecting yourself and for protecting the all important spell casters behind you. Secondly, you can make more than one attack of oppurtunity per round which is potentially as good as cleave for generating extra attacks - especially if the DM is fond of pulling dirty tricks like grappling, disarming, tripping, sundering and so forth (which he should).
3) Spring Attack: Again, this feat gives you two worthwhile advantages. First, you can attack a large creature or any other creature with reach and not provoke an attack of oppurtunity by moving in his threat zone. This is huge in itself. Secondly, you can move away from any creature with multiple attacks and prevent it from making a potentially devestating full attack action against you.
4) Hold the Line: The ability to get an attack of oppurtunity whenever you are charged is huge, and can save you or at least mitigate the disadvantage in that all important surprise round when you are flat footed, but your foe must make a partial charge in order to attack you.
5) Close Quarters Fighting: One of the nastiest special abilities is Improved Grab, in part because you are generally at a huge disadvantage once grappled by anything that has it, and in part because it usually is followed by something even worse like swallow whole. The ability to negate a huge number of foes most potent attack and keep the fight on your terms is huge.
6) Spell Casting Prodigy: Again, another feat with two worthwhile benifits. You get at least one extra spell (at some point), and the DC of all your spells increases by one.
7) Spell Focus (Enchantment/Necromancy/Transmutation/Illusion): It's hard to beat making the DC of a game breaking spell 2 higher than normal.
8) Expertise: If you are a fighter, the majority of foes you will fight have a fairly low AC compared to your attack bonus. This means that you will almost certainly hit them. On the other hand, few foes are almost certainly going to hit you because your AC is probably on average 5-10 points higher than most monsters. If you can bump your AC up an additional 5 points beyond what is usual for your level, you can usually more than half the ammount of damage you take without halving the ammount of damage you do. It is not unusual to be pitted against foes that need 14's (or so) to hit you. If you can put it so that they need 19's (or so) to hit you, the fight is all but won. IMO, this is even more important than Power Attack. After all, what defeats the PC is generally attrition. It is more important to avoid getting hit than to do extra damage (except when the extra damage avoids you getting hit). This is especially important because it probably getting critically hit that worries the PC more than anything. As long as you survive, you can generally spend resources to continue the fight. If you get dropped, the battle can swing against the whole party.
9) Expert Tactician: This is the converse of Combat Reflexes/Hold the Line/Improved Initiative. Just as there are many times when it is important for you to mitigate the effects of being flat footed, there are many times when it is important to maximize the advantage you have against a flat footed foe. With you and your friends doing there best to keep the foe off balance, stunned, dazled and otherwise unable to take an action, you maximize your advantage by putting on the extra hurt.
10) Combat Casting: As a spell caster, you are going to be in alot of situations were you must cast a spell no matter what to save a dying friend or to get in that all important game breaking spell (web, weird, holy word, wail of the banshee, or whatever) before you are overwhelmed. This lets you reach that point when you can safely Cast Defensively any spell in your repetoire that much earlier.
There are a variaty of runners up like power attack, cleave/great cleave, whirlwind attack, blooded(!), point blank shot, rapid shot(!!), precise shot(!), alertness(!), lightning reflexes/iron will/great fortitude(!!), improved counterspell, improved feint, improved trip, improved critical, weapon specialization(!), and so forth but in general whether I'm making a PC or a potent NPC, its the above list I turn to first when selecting feats.