Starcraft 1 & 2 - Play the first if you want to experience the classic, I still play it but the graphics aren't that good anymore. The second is very similar, core RTS gameplay, and - I've heard - an absolutely kick-ass single player campaign.
Warcraft 3 - Another classic, plus it has the whole hero system. You really can't go wrong with this game, it's so fun and there's such a huge community built around it.
Dawn of War 1 - This is one hell of an RTS. Blew my mind the first time I played it and remains one of my favourite games to this day (including its expansions). Pick this if you like science fiction and lots of variety in gameplay. DoW 2 is also good, but not much of an RTS in the traditional sense.
Company of Heroes - A lot like Dawn of War set in World War 2. Absolutely effing fantastic game, featuring a cover system that I had never seen before and... it's just awesome. You won't regret having this one.
Supreme Commander 1 or 2 - Pick this if you want scale. This is an awesome game, you build hundreds - even thousands - of individual units, and have colossal battles with them.
Rise of Nations: Rise of Legends - this is a weirdly awesome game, different from your standard RTS in many little ways. Pick it if you like the combination of steampunk and magic.
Command & Conquer - Which one? Take your pick. This series is famous, and for good reason. The newest ones are Red Alert 3 and Tiberium Wars, but if you're up for a bit of old school graphics, the older games are eternal classics. Generals was different, but also kicked ass.
Age of Empires - The, classic, RTS series. My favourite is and always will be Age of Kings (more specifically, it's expansion, The Conquerors). But Age of Empires 3 is the newest, and it has 2 expansions.
Pick any one of these games, and you will experience a damn fine RTS.