Both Netflix and Hulu Plus offer streaming content for about $8 a month. Netflix is best for movies. Hulu is best for TV series. There are other apps, even a few from the major networks; like ABC. Many of these are free, but do not offer the range of content of the paid accounts. Some only work if you already have a cable subscription to their channel or network.
If you are traveling out of country you may run into blockages. Content licensing is often country or region specific, and most app developers don't like the idea of being sued.
Computer-less downloads are a tougher prospect. I'm sure there are some solutions, but I'm not familiar with any.