Pinyin (拼音) is by far the most used romanization system for Mandarin Chinese today. It is the official romanization system in China, and it's studied by all elementary school students. Learning Pinyin is an essential step in mastering the pronunciation of Mandarin and to be able to type in simplified characters.
You may also sometimes come across the Wade-Giles or Yale romanization systems, which were commonly used before Pinyin. Wade-Giles is still used in Taiwan to transcribe names of people and places. If you are reading materials from Taiwan, you may come across Zhuyin fuhao (注音符号), also known as Bopomofo (ㄅㄆㄇㄈ). This is a non-roman writing system to write Chinese pronunciation. It is not often studied by even foreigners in Taiwan (they also use Pinyin to learn). However, it may be useful for you to learn if you are interested in Taiwan as it can be found in everyday life there.