Copies allows clipboard sharing between Mac OSX and iOS using device specific versions, it uses iCloud for data sync, there's no other setup needed. File copy maximum file size is 20MB, and file transferring uses HTTPS with the developers server powered by Linode.
There is a listing of clipboard managers here.
I’ve just been sent details of two more clipboard managers, Paster is a clip board manager for both Mac and iPhone with Cloud-based synching usinging https rather than Wifi or bluetooth. It has searchable history and keyword filtering. Colective will remember: Text, images, PDFs, movies, URLs, appointments, files etc. When Collective is running, a "C" will appear in the top-right of your menu bar. Pressing ⌘-Shift-V will show Collective's history of what you have copied (alternatively, you can click the "C" in the menu bar). Clicking on any item will add it back to your clipboard, so you can paste it again. No synching between devices.
There is a list and short description of 21 different clipboard managers here. As they say choice is good.
I’ve just updated the list of clipboard managers to include Copy’em Paste a clipboard history application it supports text, images, links, HTML, code, PDFs, files and you access the clippings via menubar or keyboard shortcut (e.g., ⌘-Shift-V). You can search, delete or edit clippings and blacklist applications (not save clippings from them).