Any high speed Internet connection should be sufficient to stream videos online. The need for additional speed will come into play when you take into consideration the quality of the video you would like to watch, and if you have additional devices in use at the same time.
To stream HD video, you should aim for at least a 15Mbps service. If you would like to stream HD videos while also using your phone, a laptop, a desktop or have some other devices going at the same time, consider bumping up your speed to the higher speed packages available for you.
To stream in Ultra HD (4K) video, you should aim for at least a 25Mbps service. If you would like to use additional devices while streaming content, consider bumping up your speed to packages above this.