Based on your criteria:
1) Still playable today:
I just replayed the original version (not the remaster), and it’s just as fun now as when it came out. The graphics have aged nicely compared to nearly every other 3D game from 1999. It’s not looker anymore, but it’s still very playable. Being able to create your own Battle of Endor over and over again never gets old for me. I love to watch my bombers make attack runs on capital ships while my own capital fleet rips them apart with ion beams.
Additionally, while I generally find the adding of 3D elements to 2D games to be annoying at best and game-breaking at worst, Relic was able to use 3D here in a way that enhanced RTS gameplay. There are some cool tactics that playing in 3D space opens up.
2) Great multiplayer:
I personally didn’t play multiplayer back in the day, but apparently it was quite popular. Wikipedia states that there were over 18,000 people registered on the ladders at the height of the game’s popularity. All of the good stuff I’m about to say about the single player also extends to the multiplayer. There is also a skirmish mode against bots for a “single player multiplayer” experience.
3) Great single-player:
The story in the single-player game remains the benchmark by which I judge all other RTS experiences and is one of the best stories in a video game, period. No game has gotten me as emotionally involved in the story as Homeworld, to the point where I’d replay missions until I could complete them without losing a single unit. There really aren’t any “characters” on your side besides the disembodied voices of Fleet Command, Tactical, and your pilots/crews, but their constant chatter and announcements do a lot to pull you into the world and get you to buy into their struggle. I don’t want to spoil the story if you haven’t played it, but the journey of the Kushan people to find and reclaim their homeworld is an incredible one.
That story is also in service of some pretty cool gameplay. Aside from assigning tactics and formations to maximize the amount of firepower your forces can deliver, your objectives change up constantly and are only rarely the typical “build a base and destroy the enemy base” crutch that RTSes lean on. One of the first missions has you en route to meet up with a supply ship only to find it destroyed by raiders, which you then need to defend your mothership from. Another tasks you with destroying an enemy base near an active supernova, which throws off radiation that damages all ships unless they’re within protective dust clouds. The final battle for the homeworld is about as epic of a mission as you’ll find in an RTS, throwing wave after wave of enemy ships at you while you desperately drive to your objective.
One other cool thing that Homeworld did was fleet persistence, meaning that any units left alive at the end of a mission carried over to the next one. The enemy forces you’d face in the next mission would increase or decrease in number depending on what you went in with. It’s possible to game this system by retiring/scuttling every ship you have before moving on, but I wouldn’t recommend doing this as it considerably reduces the epic scope.
In short, Homeworld is awesome. If you’ve never played it, I’d recommend the remastered version because it fixes the one major issue, which is that the game came out in 1999 and looks it.
Like with Tetris, I wanted point out one instead of the entire genre (Dr. Mario and all). There are many RTS games that could also fit assuming if one finds them still enjoyable today. RTS is such a fantastic genre because it sports both compelling single player and multiplayer sessions. It used to be that the single player was just training mode for multiplayer. This, however, did change. Despite my misgivings about the ‘APM god for multiplayer’ for Starcraft 2, I still recommend the game to people because of the fantastic single player and many ways to play multiplayer.
Homeworld has a very strong musical score. Let’s listen, reader: