Okay, now I want to figure out what on earth we were doing wrong, because a 60 minute or less combat was the rare exception.
Though in the 3e games I played in back in the day, combats would often take the full session as well...
It's hard to give specifics, but there are some general patterns that I think really help:
1) Having, as others have said, a "crib notes" version of your character sheet, specifically geared for combat use. When I temporarily took over the Wizard, I jotted down the powers he had, defenses, etc. It helped that he mostly tried to stay out of sight and such. I'm strongly considering making a simplified "list of powers + basic tactics" file to work from during play.
2) "Lumping" similar enemies together. Got five of the same thing on the board? Give them one initiative count and roll all same/similar attacks before rolling any damage. This will mostly apply to DMs, of course.
3) Use something to represent enemy morale. A simple system checks for loss of group leader, hitting half strength, and losing the numbers advantage, for multi-person fights. For solos, consider bloodied and half bloodied to be turning points, if a solo's gonna break it will start to show by then. Basically, avoid spelling out the tail end of a foregone combat, especially if your players like to capture enemies alive rather than having a "kill 'em all" attitude.
4) Don't be afraid to use minions. Over-use is possible, but they're really nice for making fights seem scarier than they are.
5) Encourage the spreading out of resources throughout the day, while discouraging "perfectionist" power usage. It's REALLY hard to use a legitimately "bad" power in 4e, but it's also hard to get a perfect storm of effects. I've done it, but that was because the choice was easy to see (Dragon Breath onto a space with 7/9 square occupied, then pop a daily to hit 4-5 adjacent enemies and continually mark all adj. enemies for the rest of the combat? Yes please.) Such things should be rare and feel awesome when they happen, rather than being seen as the "default."
6) On the other hand, don't feel at all bad/remind your players it's not bad to use At-Wills. In that same fight as the beautiful setup, I ended up using At-Wills for *most* of the other rounds...and still felt like I was helping. In this sense, the Essentials classes are somewhat helpful, actually, because they naturally encourage more Basic Attacks. Having a very beat-'em-up style Leader, and a party that can take advantage of it, will also help there.
7) Consider, during down time or between sessions, having your group's rules buff (who may not be the DM) talk briefly one on one with each player. Stuff like, "when we get into a fight, what are your priorities? If you go last, who are you watching for a good set-up? If you go first, who do you hope will follow your lead?" Things like that can really really help. IMO, 4e is much more a "team game" than prior editions. Your party doesn't have to be a Radiant Mafia nor a crazy basic-attack extravaganza, but things will go faster and generally better if they know both what they can do for a friend, and what their friends can do for them.
8) This last one can be a double-edged sword, but having terrain more interesting than "flat, open field/empty room" can also make a big difference. That "obvious" set-up I mentioned earlier happened because the entryway funneled the attackers right at us, so they were all bunched up and pouring out from one place. Have your players think, as much as possible, about where they would best be able to use their cool moves. A Wizard wants to balance "not getting shanked" with "close enough to drop sick fires on the far side of the choke point." A Paladin (which I'm playing) must balance holding attention while not getting in over his head. Rangers will depend on whether they're melee or ranged focused. An Avenger may want one guy all alone, or may want to have all their friends join the beatdown. The terrain will influence how easy these general goal are, and players should immediately start thinking about where they can go to have the most effect. In a sense, it's a bit like learning to mentally "see" the possible moves any given chess piece can make, so you're able to see a potential fork before it happens.
Edit:
Gosh, can't believe I forgot this one!
9)
Minor actions and off-turn attacks are a "sometimes" food! If your group has timing problems, cut down on off-turn actions, and remind them that there is no shame in having nothing to spend your minor on. Minor actions tend to be relatively specialized, so it's okay if you don't use it every round. One solution I saw...somewhere...was to make an "aim" universal minor action: +1 to hit a particular target for your other attacks that turn. Simple, obviously effective, but clearly less good than a sustain or minor action attack, if available. Also helps avert the whiff effect.
Also...
10) Use later-era monster stats, MV or MM3 or later. If you played mostly early 4e WotC adventures....that's also partly to blame, WotC's early work was...frankly atrocious for 4e adventures (or so I've heard). Newer monsters are less "big sack of HP," more "fragile but nasty." They die faster, but they tear up PCs faster, too--much more exciting, much more "is this it, are we going to die?" without, generally, dying.