Warcraft 1-3, Starcraft 1 and 2, Age of Empires, Command and Conquers, Black and White (I love that game.) etc etc
Basically it's your building a base; gathering supplies and building up defenses, and an army while a computer or other player builds their base and army. Then you clash! Or you can just attack them in the beginning or whatever. It's in real time so unlike games like the Civilization series, it's not turn based. It happens at the same time.
Warcraft 3 had an extra mission where you played as one hero. Then they modded it and made DoTA which gave rise to the now popular arena based games like League of Legends.
Warcraft 2 ↓ is my favorite RTS personally. That and black and white, i just have lots of fun with Black and White.
EDIT: If you're interested in some, steam sales are going on right now so you can buy some for cheaper than normal. If you don't care about age, Good old games or GOG has some cheap strategy games too as they are having a summer sale too.





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