Valiance said:
Single player campaign: Dawn of War II or Homeworld
Single player skirmish: Supreme Commander
Multiplayer competitive: Starcraft
Multiplayer lulz: Warcraft 3 / Starcraft UMS's
I agree with this perspective, especially about Supreme Commander. The level of battlefield control is astounding. In less than an hour, I was able to tell exactly what each and every one of my 500 units were doing, and exactly what they were going to do next. The game even displays timers next to units telling you how long it will take to complete their next order, the one after that, and so on. Also, every shot fired is not pre-programmed to hit or miss, it only matters if a unit crosses its path (or rather, doesn't get out of its way).
I think the reason I like it is because it's the polar opposite of most RTS games out there. It almost completely removes the micro-management aspect of the game in favor of strategic control. You are not the pilot, you are the commander. You tell your troops what to kill, they handle the how, and the AI is quite capable of handling the unexpected.
On Dawn of War... DoW2's gameplay was loads of fun (but the lack of variety makes it a bit less replayable), but DoW1 was more traditional, and had an amazing story behind it. I recommend you play DoW1 before DoW2.
Starcraft's story is top-notch, but online competitive play is all about micro-managing. If you like microing, perfect. If not, play it for the campaign and so you'll get the ever-so-present references to it on the internet.
If you have played any of these before, forgive me for the needless text.