Generally you hear about the British, French, American, and sometimes Germans (in Africa), but did countries like India or China ever try to colonize other places in the last few hundred years? If not, why? Did they just not have the navy for it?
Huh. That is actually a pretty interesting question. When the Roman Empire conquered Germania and Britain, for example, does that count as "colonialism"? When a smaller power buys off the bigger power with tributes (e.g., when the Malacca sultanate sends tribute to the Emperor of China in the 15th century, or the Malay states doing the same to Siam two centuries later), can that be considered at least proto-colonialism?
Probably the best example is Japan, who conquered Taiwan and Manchuria before WW2, then during WW2 conquered more of China, and large areas of South-East Asia. If they'd won, they'd have kept all these as colonies.
(It should also be said that India wasn't an independent country until recently: before it was part of the British Empire, it was multiple countries. Actually, under the British Empire, for a long time, it was still multiple countries.)
But there's also a question about what exactly is Imperialism. The Chinese Empire conquered huge territories over the centuries, but as places like Tibet and Xinjiang are now simply part of China, the Chinese say this is not Imperialism. They are not ruling other countries the way Britain ruled India: it is simply now China (many Tibetans and Uighers disagree, arguing that they are essentially colonised states whose economies are set up to benefit the Han and western China by extracting materials. The Chinese government on the other hand argues that they are bringing civilisation and development to restive regions). And prior to WW1, there was the extremely large Ottomon Empire which ruled the Middle East. But it looked quite different from western-European style imperialism.