Can I sync players and worlds between multiple computers?

This can be done with Dropbox and a line in Command Prompt.

1. Quit Terraria to make sure none of the files are in use.
2. Look for the folder C:\Users\<username>\Documents\My Games\Terraria (this is the Windows Vista/7 location).
3. Move this folder into your Dropbox folder.
4. Open Command Prompt with administrative privileges by right-clicking on it in the Start menu and choosing "Run as administrator".
5. Run this command: mklink /d "C:\Users\<username>\Documents\My Games\Terraria" "C:\Users\<username>\Dropbox\Terraria"
6. Launch Terraria and verify your characters and worlds are available.
7. Repeat steps 4 and 5 on each additional computer that you want your characters and worlds to be available on.

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Another option, perhaps even simpler, is to use BitTorrent Sync to synchronize the Terraria folders on two computers. If you use BitTorrent Sync you do not have to move the folders and make links. You can sync them in-place.

GameSaveManager can detect game saves for hundreds of games. It supports easy moving of games through zip files. It also has support for syncing using Dropbox or your own Private FTP server.