There is really no such thing as an “international trademark.” But based on certain treaties, when a company files a trademark application in one country, it can file a trademark application (usually within six months) in another country.
For companies who want to protect their trademarks in foreign companies, we use The Madrid Protocol (except in Canada). Under the Madrid Protocol, you can file a single application that matures into a registration in multiple countries without necessarily having to hire lawyers in multiple countries. Renewals and assignments are also centrally managed.
If you are making money from foreign customers, or if you expect your company to be acquired by a foreign company, then foreign trademarks probably make sense.