I am working in America. My girlfriend is in Taiwan. Every month, I will transfer 800 USD to her via Bank of America. Is it illegal? Will it be considered money laundering?
Money laundering is when you try to hide where your money came from. Are you doing that? No.
If the police wanted to see where your girlfriend's money came from (they probably don't), they can see she got it from your account by a wire transfer. And if they have a good reason, they can ask the American police to look at your account and see that you got it from your job. They might even interview you, and you'll say "yes I work at this job and I send $800 to my girlfriend every month."
Since they could easily trace the money if they wanted to, it's not money laundering.
Ok, so it wouldn't be illegal to transfer money to your girlfriend in a different country, unless its Laundering. Money Laundering is when you transfer money across the world for illegal activity, and you try and hide your transfer. However if your transferring it just to give her money to buy legal items, then you should be good. Also following up with what user253751 said, All Law Enforcement in different countries can track wire transfers, and even though most of the time its none of their business, if they suspect something, they can pull up your bank records. So if you just want to give your girlfriend legal funds to spend on legal items, then it should not be a problem.