The Tomboy notes app built into many Linux distributions can synchronize across platforms through WebDAV or SSH, but it's easier to set up your notes to be automatically synchronized through a Dropbox account.
The Starry Hope Productions blog explains the relatively simple tweak needed to start up the synchronization. Open Tomboy's settings, set the Synchronization settings to Local Folder, then change the folder path to a sub-folder in your main Dropbox folder, usually located in your home directory. From then on out, hit "Synchronize Notes" from the Tools menu on any note, and your data is safely shuttled into the cloud.
Want to grab web notes and instantaneously drop them into Tomboy, and then Dropbox? Try the Tomfox Firefox add-on. For another great Dropbox syncing trick, try making it your ultimate password syncer.