Change default text editor to Sublime Text in Linux Mint

Open /usr/share/applications/defaults.list in Sublime:

sudo subl /usr/share/applications/defaults.list

Search for all instances of gedit and replace them with sublime_text. Save the file, quit Sublime, log out and back in, and you should be all set.

EDIT

While the above instructions should work with any .deb-based system (I use Ubuntu), apparently there is an issue with Mint where changes to /usr/share/applications/defaults.list are lost upon reboot. To work around this, do the following:

1. Create a new file (if it doesn't already exist) called ~/.local/share/applications/defaults.list in Sublime. The first line should be [Default Applications].
2. Open /usr/share/applications/defaults.list in Sublime. Hit CtrlF to open the Find dialog and type gedit into the search box.
3. Hit AltEnter or click the Find All button to select all the instances of gedit in the file.
4. Hit CtrlL to expand the selections to the entire line, then hit CtrlC to copy the lines.
5. In ~/.local/share/applications/defaults.list, hit CtrlV to paste the lines containing gedit.
6. Hit CtrlH to open the Replace dialog. Search for gedit and replace with sublime_text. Hit CtrlAltEnter to Replace All (or click the Replace All button) and you're all set.
7. Save ~/.local/share/applications/defaults.list, log out and back in, and Sublime Text should now be your default text editor.