So here are a few ideas about making combat less time-consuming and Not Fun. I'm not sure any of them are a perfect solution, but they each have merits.
Make Combat Simple and Fun. This is the "Savage Worlds solution" in my mind, which to me is a near-perfect example of combat stripped to its essentials. Most bad guys in SW are explicitly goons, so they go down quickly, and only the "boss" of a given adventure has more sophisticated powers (and durability). The dice mechanics in SW are a lot of fun, too, with "aces" giving you a real rush as you blow the top off a roll. SW does have some issues, though -- the dice rolls are fun, but swingy, and they can make things go to shit for the players fast. And for myself, having player characters possibly missing actions for several rounds is the essence of Not Fun.
It's also worth mentioning that the same simple, fun philosophy underlies a lot of the Old School Renaissance games. On paper, they have a level of intimidating complexity -- what modern game has tables and combat matrices? -- but in play most OSR games are straightforward. Roll your attack, roll your damage, move on.
Make Combat a "Sometimes" Thing. I used to have a rule of thumb while in the Big Chair that I shouldn't run more than two combats per session. These days, it's one or none. Simply eliminating altogether combats that aren't significant to the overall story or the characters means you aren't wasting your time killing orcs or stormtroopers no one cares about.
This is what I've been doing in my current, climactic arc of Sunset Empire -- essentially, if the PCs aren't fighting a villain with a name, we don't bother with the details of how they meet their fate. John Hooke the 'golemnaut' facing his nemesis in the body of the Golem of Prague is an important fight we need to roll dice for; the players dispatching an army of faceless vampires, not so much. We can simply assume the players overcome the goons and move on.
It's worth mentioning that this kind of philosophical approach to combat -- deciding what's necessary -- is something that you need to use a deft hand with. I feel that I probably should have thrown in a little more fighting than I have, just to put stress on the players' resources. Finding the "sweet spot" of an amount of combat that's "just right" is something that might take some practice.
I think games like Wild Talents (and other One Roll Engine games) that make combat fast and dangerous fall under this banner too. There have been plenty of games in the past that make combat deadly enough to discourage players casually going for their guns (although it happens a lot more in Call of Cthulhu than you'd think), but few that make the actual mechanics as smooth and fast-moving as ORE.
Not Combat Resolution, CONFLICT Resolution. This is a solution that a lot of newer games, especially "indie" games, have embraced. Instead of working out every blow in a fight, you resolve the whole combat with the mechanics. Primetime Adventures uses this philosophy, as do some of the Cortex Plus games. This has the dual utility of reducing the amount of mechanical weight placed on combat and giving equal mechanical representation to other forms of conflict. So whether you're punching it out or shouting it out in Smallville, the mechanics are the same, and the idea is to work out the character issues rather than mark off hit points.
I've played around with this idea in FATE too, extrapolating off the mechanics proposed in Starblazer Adventures. Although FATE does a good job of making goons easy to bust up, combat can be draggy. I have been experimenting with creating stat blocks for whole Action Scenes the players have been interacting with, rather than dealing with individual bad guys. So if the characters were caught in an ambush by imperial marines, "taking out" the scene by inflicting enough stress and consequences would end the fight. This works pretty well, because it allows players to really make a big swing in the events by paying off a big roll (and FATE seems intended to reward players setting up Aspects then knocking the bad guys out with a single big hit that cashes them in). It also allows the GM to arbitrarily pull the plug by declining to apply shifts of stress to Consequences, when everybody's had enough fighting for today thanks.
It's worth noting that, as my friend Rob has said, "Sometimes the conflict is the conflict." In other words, in a game like PTA that resolves interpersonal conflict rather than maps out specific interactions, sometimes you can be in the not-ideal situation of building up to an epic fight that is not played out in the mechanics. In PTA, one draw and you're done (there are optional rules to address this, but still). This is a sticky point with Conflict Resolution mechanics -- although they can speed you through unnecessary fights or consign them to background colour, sometimes you do want a little more detail. It's tricky finding a perfect middle ground.
Again, none of the above are perfect solutions -- just stuff we've played around with in the last few years. I think ultimately how much combat you have in your games, and how you negotiate how much is too much, is something that has to be figured out on a group by group basis.