It is a common fruit here, though not the most common. They are much bigger here than in the United States, and have many more varieties. They are much sweeter, too.
Fruit was one of the things I was most excited to eat when I got to Taiwan, and it is the first thing I bought upon arrival. There are so many common types: pineapple, passion fruit, guava, lychee, avocado, so many types of mango, pomelos, Asian pears, persimmons, oranges (which are green), papayas, watermelon, bananas, dragon fruit, imported apples, custard apples and starfruit.
Shocked! It was so much sweeter and juicier than mangoes that I am used to. In the United States, mangoes were my favorite fruit -- and I didn't even know they could get so much better! Here, they are so big that I could eat a mango at noon and not be hungry for lunch.
I also felt very connected to Taiwanese people. They take great pride in their fruit, calling Taiwan "The Fruit Kingdom" with a knowing nod. It's common to grow mangoes near your house, and it is common to see mango juice, tea and jelly along the street.
I buy my mangoes at the morning market. There are fruit vendors who sell their fruit only in the morning, which is usually cheaper than the vendors who are open all day. Basically, all vendors are cheaper than all super markets. I buy them whole, untouched, and usually don't wait long before going home, washing it and slicing it open. There is so much meat on the fruit that I usually have to share it with my roommates!