I can strongly recommend Dropbox, which I use for exactly that purpose, and have done for some years without any problems.  You get 2GB of storage free, which enough for most of us unless you are wishing to share lots of video, pictures and music.  Beyond that it is one of the more expensive options, but you can get extra free space by recommending others (in fact if you use the link to Dropbox in this email to try it out, I'll be rewarded with some extra storage, so please don't hesitate!).

I does work well, and means that all my work is not only available on both my computers all the time, it is all backed up in the cloud (on the Dropbox website) and I can access deleted documents if I need to.  I can also chose to share a particular folder or document with a specific person; this has proved invaluable when working on some projects with a colleague who works miles away, or overseas.

Dropbox's success has spurred the creation of many competitors- Google Drive, Sugersynch, Insynch and many more - you can read an analysis here, although the review is a year old.