It’s not illegal to use a VPN for streaming, but you need to make sure you comply with the terms and conditions of the service you're using. For example, the Netflix terms of use(new window) say:
“You may access the Netflix content primarily within the country in which you have established your account and only in geographic locations where we offer our service and have licensed such content”.
So using a VPN to watch content that’s not licensed for the area you’re currently in is against Netflix’s policy. However, you have a right to watch content you pay for and can normally access when you’re home.