Command & Conquer: Tiberian Dawn did for the RTS (real-time strategy) genre what Doom did for First-Person shooters. That is, the game was so darn successful that all the other game companies said "Hey! I wanna make one of those stategy-thingies!"
C&C's main highlights were its superb use of in-game music to create atmosphere (featuring an interactive playlist!), between-mission cutscenes that were well ahead of their time, and the absolutely frigging brilliant installation sequence. I haven't installed a game before or since that put so much effort into impressing you during installation. You were sucked in before you even started the game for the first time.
C&C's downsides included a pathfinding algorithm that could be a little disappointing at times, and a poor sense of balance between the two "sides". The GDI was superior to NOD in the majority of situations, simply as a result of having better units (can anyone say "Orcas"?), and NOD had far more difficult single-player missions. They could have worked on this a little more. For good side balancing whilst maintaining an interesting set of distinctions, see StarCraft, Total Annihilation, and recently, Command & Conquer: Generals. C&C also had a fairly mediocre unit AI. For example, if you surrounded an enemy base with sandbag walls, instead of destroying the walls with great ease, the enemy just got stuck behind them, cutting off their resource collection etc. Many's the time I used "sandbagging" to win single player missions. It's not really a challenge, but has good chortle value. For an example of good, sophisticated AI, see Dark Reign. However, given the amount of new ground C&C covered, we can really forgive the development team for these drawbacks.
Over and above the pros and cons of the game's design, C&C was fun to play, both in single player mode and against other people. That's what really makes a game stand the test of time, and what makes this one a fond, firm favourite for so many strategy gamers.