Consider a 3 axis nomogram. One axis is "Tactical Complexity" another is "Narrative Complexity" and the third is "Time spent" These axes need to be calibrated for your group, obviously.
A good, entertaining, tactical combat is its own reward. It moves (relatively) quickly and has engaging amounts of tactical complexity.
A well narrated conflict is also its own reward: creating dramatic tension and resolving it based on the actions of the characters.
One problem is that (to take a system that is quite guilty of this) 4e combats do not contain any narrative conflict. While enemies have the pretense of conflict, the system provides for one outcome: complete player success at the cost of resources. While TPK threats make for tension on the player's behalf, the threat of the TPK is desire, and an actual TPK in any long-running campaign is a complete FUBAR and something to be avoided.
Therefore, all the interesting choices happen at the tactical level. While people may certainly choose to dress up actions in narrative description, It more than doubles the length of a fight: paying attention to the narrative means that people aren't thinking about their next move. At the same time, there are no interesting narrative options in a standard set piece battle. The players have the objective: eliminate the opposing forces, dictated by the conventions of the genre, and the monsters have the objective: try, but not too hard, to win. The monsters are an interesting tactical problem, and superbly uninteresting narrative problem.
(taken from discussions with @Magician)
You can increase the narrative seeming of the combat-without-conflict by allowing players to narrate their attacks. In my wave game, I provided floating "+2 bonus bennies" to people who had entertaining narration of their combat interactions. These bennies could be used on any subsequent roll for any purpose, though not stacked.
Through this, I established a tangible reward that provided interesting RP opportunities. At first. As the game progressed, the RP aspects were more and more an afterthought. Doing this in a live game will significantly increase combat length, however.
Another option is to introduce real conflict into the combat. This is a project I'm currently working on with a friend. From our initial thoughts and experiments.
The way to introduce conflict is somewhat stylized and is the enemy of set-piece battles. Each side must declare their goal for the battle, a goal that if the enemy wasn't there could be met easily. (Therefore no goals of "kill the enemies"... most of the time. Even in big-boss battles, presenting a compelling conflict can be more interesting than simply "I kill the big bad"). Establish formalized victory conditions such as "everyone has to be past this door", "someone needs to burn the rope", etc... Then, allow players to narrate skill uses towards the accomplishment of these goals, much as how the fourthcore adventures allow early exits from incredibly deadly combats when alternate tactical victory conditions are met.
By providing conflict, a tangible benefit to narration, and a reason to not simply wail on the opponent, players will have far more interest in spending their standard actions on something other than simple damage. This provides mechanical support for the narration of taunts (keeping enemies from moving towards their goal-area by making them enraged) interesting movement (swinging on ropes! Awesome! Not pointless!) and all the rest. The early-completion goals mean that combats time won't be trebled.
If the enemies achieve their victory? Allow players to spend 1 HS to deal an enemy's bloodied value to itself and then to narrate how they finish off the enemy. The conflict has completed and prolonging the combat is pointless. This provides narrative reasons and tactical reasons for narration and firmly establishes the narrative conflict's dominance. It also gives the GM headaches, cause prepping encounters on the fly is so much fun in tactically heavy games.
I'd be happy to test your implementation of this advice in chat, for extra data.