I'm using just that: A 1GB online storage device that uses webDAV. Works well with linux (using libneon or davfs). webDAV is an apache mod so it's pretty standard and I guess a lot companies offering such a service will use it.
The service I use is provided by gmx (www.gmx.com
). However, this is a company based in Germany and I'm not sure how well international billing is handled. Apple offers the idisk for .mac users which uses webDAV as well, but they use plain http rather than https. You can always use stunnel for added security, of course.
I've heard about xdrive.com but I have no experience with their service. Try googleing for "online storage webdav" or something like that. I've seen some text ads there that looked pretty promising.