Certain services work best with certain types of mobile gadgets. For example, Amazon will stream video to almost any tablet, but it works best with Amazon's own Kindle Fire. However, it doesn't have a smartphone app, while Netflix does.
If you already have a mobile gadget, or are planning to purchase new ones, make sure they play nice with the services you use.
Mix and match
There's no rule that says you have to choose just one of the options above. You can stick with cable for now and gradually explore free streaming video services.
Ease your way into it and find out what works and doesn't work for you. Take advantage of the free trials that the major streaming services offer.
Don't forget that cable companies want to keep you as a customer. They're upgrading their services and trying new promotions to make their offerings more attractive.
You can leverage this into discounts and savings. For example, you can often get customer service to drop the monthly rental fee for your cable modem.