In my campaign, the single greatest cause of slowing down combat was kibbitzing. For instance:
I'd call for everyone to roll initiative and then we'd start. Invariably, the first person to go would state: "I am going to move here and then I'm going to try to slash the enemy with my sword"
However, the wizard would then groan and say: " No, don't do that, because on my turn, I am going to cast a lightning bolt, but you will be in my way"
And so the discussion began. Thirty minutes later, we would finish the first round of combat. We were typically getting through only three encounters a night. (Sure, if encounters include lots of role-play, I can see where this would be fine, but in a dungeon crawl, where the PC's are simply attacking everything that looks threatening, three encounters in 7 hours is horrid)
I then starting re-reading the faux encounters in the PHB and the DMG, and I noticed how smoothly the encounters seemed to go. I noticed right off the bat that there was no kibbitzing from the other players. The DM would simply ask what a character was going to do, and that is what the character did.
So, I introduced the "no kibbitzing rule" in my campaign. It has had two immediate effects:
1. The group is now making much better progress in combat encounters.
2. After an encounter is over, the characters debrief and talk about what went wrong and what could have been improved. Slowly but surely, they are developing tactics on their own, and it has made combat encounters much more strategic and interesting. In short, they learn from their mistakes. Before I introduced the rule, they did not learn anything, because they did not have to. In addition, they have all started reading more about the multitude of things they can do in combat:
Trip
Charge
Grapple
Melee
etc.
It has changed our tactical encounters from toe-to-toe brawls to much more coordinated efforts. The characters are thinking more than they ever did before.
3. The players are no longer creating characters that only specialize in Smack Down melee or "nuculur splosion" casting. Once they recognized that improved tactics require diverse skill sets, they started thinking about being able to use more than one kind of weapon and being able to cast utility spells more often. This has certainly improved their survivability.
So, the "No kibbitzing rule" has had a number of positive benefits to our game, but it has definitely helped pick up the pace.