Is there an Apple app that lets me view videos?

I'm able to watch YouTube videos, most videos from TV network websites (interestingly, I can usually view them on my devices but not my computer), the video player on SpoilerTV.com and occasionally videos embedded in TVGuide.com articles. But I have come across videos that just have a blank area or black box where the video should be on my iPhone 5S and iPad 2. Some even say that the plug-in isn't supported. I don't always have time to watch them on my computer so I'm wondering if there's an app (preferably free) that'll let me view the videos. My brother suggested the Dolphin browser but the ones I found were for other devices or operating systems or something like that.

Added (1). I have no idea what kind of videos they are. I just know that sometimes on sites like TVLine and TVGuide, the video players they use have a certain plug-in that Apple devices don't support. Meaning I have to wait until I'm on my laptop (with Windows) to watch them, something I don't always have time to do. I want an app that'll let me view these apps on my devices anyway.

Can you please explain more? What type of vids do you want to watch Twitch etc…