Get player buy-in on the idea that turns are for acting, not for thinking about what to do. When it's time for a character's time in the spotlight, the player goes
immediately or offers to delay his or her turn. Alternatively, the player can ask for a suggestion from fellow players, but must take the first serious offer that is made - this isn't a time for brainstorming until the player hears something he or she likes. This simple method cuts down significantly on how long a combat takes which means time for more content. It also means that any given player isn't waiting very long for his or her next time to shine. These are selling points for players and DMs both.
Prior to each player's turn, the DM can re-frame the scene in pithy and exciting terms. For example, "Ragnar just cut down the orc shaman, but two warriors rushed him to seek vengeance. A bowman sixty feet away is taking aim at you while two more are charging up from the flank to get at the wizard and cleric and will be there in mere seconds. What do you do?" This cuts down on players asking questions instead of acting boldly. It also underscores the frenetic tempo and chaos of battle.
I'm also a big fan of countdowns. I also very much prefer
scenarios where all pillars of the game - combat, exploration, and social interaction - come together in the same scene.