There are a variety of options - depends on what you are after.
For example, you can mount a WebDAV volume direct from the finder, so any hosting service which offers WebDAV support will let you do that. That will work directly from OSX - no additional software needed. The menu option is "Connect to Server" under the "Go" menu. If you select that now (well, after you've finished reading this) and then click on the help button, you'll get a load more information.
Another option is to use MacFuse. This software lets you mount different types of storage and services so they appear as standard Finder volumes. MacFuse allows you to do this in general, then you need another layer of software on top of it to actually mount a specific file system. I use one called sshfs. This lets me mount directories I can access using an ssh account so they appear as volumes on my Mac. So, once you are using this software you need to find a hosting provide who gives ssh access and you can then use that to do what you are after.
Sorry, I haven't used any services which make use of this so can't make any recommendations, but I've used both techniques with my own storage and they both work well.