I have a ton of songs, tv shows and movies on my iPad that I can not sync all. Can I use dropbox to put all of this onto their service, that way when I am traveling and what to watch a movie that I could not store on my iPad I can download it with out syncing to iTunes? Basically if I watch a movie on an airplane and then at the hotel want to watch another movie that I could not sync because of storage, log into dropbox, put the movie I just watched into dropbox and then take a movie from dropbox and put it onto iPad.

Yes that should work. The main issue would be the time of transfer.

why can't you sync them? Any media iPad can natively play, can be synced via iTunes

I can sync them via iTunes, but I have so many movies and tv shows from iTunes they will not all fit on my iPad because of space. So I have to choose what movie or tv show I want and then i am stuck with that until I get back into town and sync again. I was looking for something to store all of this and then when I travel I can log in and change the movies or tv shows with out syncing to iTunes.

Air Video is the streaming solution that works best for me. Try this free version first.
Don't even have to convert as it's all done on the fly as it streams.
I say why take up precious space on my device for a 1gig movie that I will only watch once....

Then there's always OrbLive with similar functionality.