I am not a slingbox person so please bear with me and correct me when I'm wrong. Slingbox literally controls your TV and redirects that signal to your mobile device. So in theory, if anyone was trying to watch that TV at the same time you would have to watch the same thing. This is good is you want to watch broadcast TV while it is broadcasting or something on a DVR (or even a DVD I suppose). If that is what you are trying to do, I don;t think you have any other options.
Alternatively, if you want to watch stored content (very much like a DVR) than you are looking for something like Hulu (for TV) or netflix (for movies or DVD TV). Neither of which are currently available for android, natively. But both are rumored to be coming very soon.
However there is a work around. I am currently watching both of those services on my motorola Droid 2, using a PC software called playon. This software runs as an intermediary between the phone and the streaming service providers (as well as more than 50 other steaming providers). Of course this would require your PC remain on all the time, much like your slingbox would need to stay on. The benefit is that you are not consuming a TV when you are streaming. (among lots of other benefits).
Playon is/was not specifically created for phones, and costs a lot more than a typical phone app. But if you were going to spend money on slingbox anyway, this might be worth looking into if slingbox doesn't fit your specific viewing requirements. Remember that there are 2 components to playon, the phone app which is free, but useless without the PC software which is not free. You need both.
