It's practical for banking stuff.If you want to open an account in Taiwan, it's highly possible the bank teller would ask you for your stamp if you want to activate "Joint Passbook Savings" service(通儲), which allows you to withdraw/deposit money in any other bank branches they have.
It's required for many legal documents.
Let's say if you have to sign your lease, you will see the signature bar says "簽章".
簽 stands for signature. 章 stands for stamps. And your private stamp is considered more powerful in our legal system. (Well, it's changing, but we basically recognize stamp more than signature)
It's not expensive which makes it a good souvenir as well.
A wooden signature stamp only cost you around 50 NTD (less than 2 USD), usually you could fetch it at the day, or a day after. Of course, it could be pricy when you pick some valuable stones or rare wood to make it.
It's cool to have your name in Chinese anyway!
Come on, I know to write your name in Chinese might be a painful job. It will save you a lot of work if you stamp it. You can choose a font you like to make your own signature stamp. Usually bank requires a font which is readable and clear. However, you could choose some funky calligraphy ones to build up your character.
Where to find a signature stamp maker?
Usually you will find a tiny small shop near neighborhood instead of business area.
It often runs business with key making. Try to search "鎖印行" near your place. Or maybe try to ask the bank tellers, they may know the closest one. (Say:請問附近有可以刻印章的地方嗎？)
Key Words/Sentences which might be useful
(put them in translator so you will know their pin-yins)
印章 Signature stamp
Hello, I would like to make a stamp.
Is that for the bank service?
Yes, so I would like the font which is clear, no special font. How much would that be?
It would be 50 for normal font. Please write down your name here.
Done. When can I pick it?
You can have it any time after 6 p.m.
Should I pay first?
Yes, and bring the receipt later to collect (your stamp).