One thing I have found to be tremendously useful for speeding up combat are combat sheets. These take a lot of prep time but make the actual combat run very smoothly. There are many different versions out there including the ones available in the DM screen pack.
What I do is make them on excel ahead of time customized to each combat.
First is an iniative order
So one column has a list of all possible iniatives usually -2 through 31. Each block in the column has three rows to it - in the event that there are multiple characters with the same iniative.
Then each subsequent column (from L -> R) is a round. Abbreviations such as AS:MM - for Arcane spell: Magic missle are used in each box.
AS=arcane spell
DS=divine spell
MEA=movee equivalent action
SA=standard action
att=attack
FA=full attack
etc.
A printed out spread sheet with this makes combat go more smoothly because all combatants will already be ordered in order, the duration of spells can be easily measured (if necessary), and a clear view of everything that is going on is right in front of you.
Depending on the number of combatants, the number of rows may have to be increased, per iniative count. THis is very simple though to do in excel.
The second thing that I don't do personally, but my friends do when they DM, is make statblocks on notecards for each NPC. Rather than having to pull out the MM or the actual character sheet of every NPC, have a stat block with all of the relevant info for battle tailored against the PCs. Such cards include BAB, HP, Init, BS, AC ST, Ability scores, weight carried, extra weapons, spells available, SA, and combat relevant feats. So for a rogue you would have a bunch of his skills like bluff, hide, MS, UMD, SM, his SA dmg, his BAB, HP, AC, Init, Speed, relevant magic items that are not already accounted for in any of the above information, and feats if relevant.
I don't do this because I typically not only plan out encounters but already have strategies that the opposing side will use against the PCs based on the common tactics of the PCs. Therefore, most of the info is in my head. Sometimes this can defintely slow things down though. And I would not recommend doing this unless you are very familiar with the enemies abilities.
Lastly have your players make all rolls at the same time. For example, if a fighter is attacking with his greatsword using a PA, have him roll the attack roll, dmg, percent miss chance if concealment, etc. all at once. This saves a lot of time. Also, I don't know about other gamers, but I always find that my darn dice always want to roll off of the surface I am rolling on. Getting something like a shoebox cover, or a board game box to roll in saves a substantial amount of time when you add up the amount of time saved by not having to find and pick up that lone black d8 under the dark table for your mace dmg.
I personally would be against doing anything that actually alters the rules to speed up combat. Hey, do what works, but for me, I find that the above 3 things tend to make combats go a bit faster.