I've actually been trying that one out recently, and I really enjoy it. At first I was a little wary of its streamlined empire management and the exclusive focus on military conquest for victory (I like crunch and detail in turn-based strategy, just not in real-time strategy), but after I figured out how to play it and went for a few rounds, it won me over as actually a rather refreshing entry in the 4X genre. I love the combat, as well, though I've only managed to play it at a low strategic level so far.
I just wish I had purchased it during the recent 75% off sale at Gamersgate, instead of the earlier 50% off sale :p
I don't have the Argos Naval Yard thing that just came out, just the collection with the first two expansions.
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Lots of interesting suggestions here, I'm reading up on some of these. There are definitely some titles here that I've dismissed out of hand as tank rush games.

As someone who also hates RTS base building and micromanagement, the games i've enjoyed have been:

Hostile Waters
(on GOG) It has a little gathering, but no base buliding, and very little micromanagement.
Homeworld
it has some resource gathering, but it has persistent armies so you don't need to build things up each mission, plus it has no bases as such.
Kohan
It kinda has bases, but you just make addons rather than placing bases, etc. Don't remember it having resource gathering. More about formations.
Warzone 2100
(freeware?) It has a fair bit of gathering, etc.. but you do get to carry over a lot of units, so you don't have to build everything from scratch.
Ground Control
This was almost an awesome game, i loved the first few missions. but it has no in-mission save, which turns later missions into frustrating trial and error restart-fests.
I uninstalled it about 50% of the way through as it stopped being fun and was wasting my time. Unfortunately GC2 seems to be more like Command & Conquer, but i don't think it has bases, and it does have a save.
Battlezone is also popular, but i haven't played it.

Try World in Conflict and it's expansion pack Soviet Assault.
Oh, and Ground Control 2 is also good.
EDIT: You could also try Darwinia.

Actually, you MIGHT enjoy that one - sure, there IS basebuilding, but the whole gameplay is about pushing the enemy back, securing points and sabotaging enemy. It's more action-ish than strategy thou. Oh, don't play Necrons. It's not that they're bad, problem is they usually don't need to expand that much :D
Or already suggested Dawn of War 2, where there's no basebuilding at all - but singleplayer is really as far from strategy game as you can get and multiplayer is ... well, you'd have to try that yourself :D
Another game of interest would be first Ground Control - it's distributed free and there's no basebuilding at all, you just choose units at the start of each mission.

A lot of people are mentioning the Ground Control series, and it's definitely worth looking into. The first one, especially, is good for someone who's in it all for the tactics and doesn't want to bother with resource management or base building at all. There's absolutely none of that. At the beginning of every mission, you get a certain amount of space on a certain number of dropships that limits how many units you can deploy to the field of battle. You choose what units you want to bring, depending on what you can reasonably expect to encounter on the ground.
And that's it. At your discretion, you can choose to deploy all your forces at once, or keep some units back as a strategic reserve, but basically, what you allocate at the beginning of the op is all you're going to have, so you have to shepherd what you have carefully. Your command APC can field repair your vehicles, and if I remember right, you can equip your infantry with medkits so they can heal, too, but if a squad is killed in action, or a vehicle is destroyed, no replacements. Difficult, but it does also mean no nonsense with constantly clicking to build MOAR SCHTUFF.
Ground Control 2 kept much the same formula, but introduced a bit of a resource gathering system, wherein you earned resource points by capturing strategic locations. These strategic locations did double duty. Capturing and holding these points got you these resource points which you could use to purchase reinforcements, and they also served as landing zones. Without an LZ, you could buy more units, but you couldn't call in a dropship to have them delivered, anywhere. Resource points could also be used to upgrade your dropship, which I thought was a neat touch. In the first game, the dropship was purely a transport vessel. In GC2, the dropship could linger for a few seconds on the battlefield. Not for too long (even with upgrades to the fuel capacity,) but those few seconds could be used to have the dropship provide some pretty significant air to ground support.

I was just thinking about this the other day after trying the 2160 demo. :)
Looks like I've got lots of stuff to try.

You could also -cautiously- try Stronghold/SH Crusader. Sure, you have to collect resources, but it's... different from the plethora of Starcraft-clones.
For example, you don't train a large bunch of peasants and send them to cut wood, mine iron etc.; it's more like the Settlers games in this aspect: you build farms, woodcutter's huts, quarries and iron mines and people from your "peasant pool" (which you can expand by building additional hovels) turn into people to staff those buildings.
Also, you don't (for example) pay 500 food and 200 wood to recruit a group of archers and swordsmen. Instead, you produce weapons in your weapon maker's shops (fletcher's hut, forgery...) and only pay gold to recruit the needed troops, which get equipped from your armory. Soldiers are also converted from peasants, but peasants drafted into the army get replenished (as opposed to craftsmen).

I'm reading a bit about World in Conflict, and it sounds sort of weird - apparently you choose one of four battlefield roles (air, armor, etc.) and primarily control units that fit into that role? That sounds like an interesting idea in multiplayer, but I will almost certainly never play a multiplayer match - how does the game work in single player? Do you control a more balanced force, or do you have to rely on the AI for your air / artillery / whatever support?

If DoW2 is something you might be interested in, Company Of Heroes would probably be to your taste as well

Tried the demo of World in Conflict last night and had a blast; I had a bit of trouble keeping up with all the click-spamming for all the unit special abilities and fire support and such, but it was intense and a lot of fun. I especially liked the way the battle was set up as a narrative event, rather than just a map with a mandate to destroy the enemy - it made the mission a lot more interesting.
I clearly have more stuff to try this weekend.

To make clear, you are not pigeonholed to pick only things that apply to your role since an infantry can purchase air role or tanks but at an increased price. So, infantry can buy some APCs from the tank role so you can use those to bring your troops to battle in style.
Also, single player is more of a practice for multiplayer but it has some fun missions. However, if you are not going to play online I will suggest not buying it since that's the real fun part of the game is the online fighting since it is like playing Battlefield 2 but as an RTS.

Company of Heroes:
There is some base building, but you'll usually only build 5 or 6 buildings during a single game. It's more focused on tactics to control a map and resources which are represented by control points that your infantry can take.
In my opinion Company of Heroes is THE BEST World War II RTS out there. Minimum base building and a ton of action.
I also recommend any of the Total War games. There really is no base building unless you count the turn based strategy parts as base building, but when you get into battle, you only command units. Those games are very much for the people who like mostly historically accurate games, or very tactical play.

One more suggestion not present here (well, if you can acquire it, that is): Praetorians. It is quite an interesting strategy game, and there is virtually no base building in it. Instead, you have to manage groups of units you get from your villages.