While RTS (Real Time Strategy) games have gone through an immense boom for their genre in the past decade or so, very few games have even attempted to bring strategy to a completely 3d environment. Even fewer have succeeded in making it look good, and visual astonishment is indeed one of the primary reactions to this game, built by Relic Entertainment / Sierra.
In a Battlestar Galactica-like setting, your race must build and protect a fleet to journey to your long-lost homeworld. The combat (and strategy), unlike Homeworld's previous resource-balancing-focused 2d cousins, plays by far the biggest role in the game. You have only a single resource to gather - Resource Units, or RUs - from which you can construct any ship from minelayer corvettes to interceptors, to bombers, to frigates, to destroyers, to carriers... etc. The immensely different possibilites that exist for fleet structure and strategy make for stunning, space-opera battles (which I tend to lose since I'm spending so much time admiring the view).
One of the biggest disadvantages of any 3d-strategy game is successfully building an entirely new interface that minimizes the obstruction of the gorgeous view while still being complex enough to handle all the move, attack, harvest, assemble, and formation commands you'll need. Homeworld pulls this off very well, as most of your commands can be issues using the mouse and a handful of keys. The learning curve for said interface, however, is probably the biggest drawback to the game; it's a little complicated. Once you get the hang of it, though, it's well worth the effort; it's so slick and intuitive that you'll be floating your camera around beautiful space fleets in no time.
Music is another big bonus for this game. They really blow you out of the water with the opening song, and every other theme - from battle music to plain old background songs - are exotic yet appropriate, making for a very enchanting experience.
The single player campaign is challenging, but fun and story-driven - particularly due to a unique series of black-and-white cutscenes that Relic inserted between missions to update you on plot developments and familiarize you with the HomeWorld universe. The original and the sequel campaigns are very similar, but both worth playing in their own right. (There's nothing quite like the backdrop for the final mission of the sequel's campaign...)
Probably the biggest drawback, and one that keeps Homeworld from really becoming an insanely popular game, is that multiplayer - while fun - is almost too strategy-oreinted for casual players to be entertained enough to play it with any dedication. Hardcore strategy gamers will be enthralled with the myriad of possibilites and in-depth tactical opportunities, but it takes serious work to become good enough to compete seriously on the internet.
I would highly recommend you play both games. Although I believe only the 2nd one is available over the network, you can find the Game of the Year edition one at most electronics stores for $10. (If you can't tell already, I think it would be worth it... :)
Someone should probably post some bad things about Homeworld, since I seem to be too strong of a proponent of the game to give a fair and balances review.
AlexBobbs also likes HomeWorld. It's really a rare type of game that transcends the rules of the genre and feels far more original than most games out there. The interface is wonderful and the overall look and feel is something that just has to be seen to be believed. My main complaint is that the structure of the single player game can be rather punishing. The campaign is continuous (you take all your units with you into the next mission), and if you don't do well enough at keeping your armada large and powerful, some levels are flat-out impossible and you pretty much just have to go back and replay levels you already beat, or start over.
DuctTapeGuy needed something to play over the summer, so he picked up HomeWorld 2 and was not disappointed. The single-player campaign is not easy by any stretch of the imagination, and playing over the internet promises nothing but ReamStick, but even so, it's a beautiful game with spectacular graphics (and graphics don't normally pull much weight with an AngBand fan!). If nothing else, however, it is sheer fun to build a vast armada, put it in a cool-looking strikegroup formation, and fly it at enemy fleets and watch them crumple like aluminum foil. Maybe someday I'll actually be able to use minelayers and defense field frigates....