When trying to set explorer to open .txt files with Sublime Text 3, I couldn't select Sublime Text at all. After browsing for the sublime_text.exe, the list of programs still didn't show Sublime Text as an option.
It seems that Sublime Text 2 had left the registry in a broken state. The solution for this is to install CCleaner and running the registry cleanup, TWICE. After that, reinstall Sublime Text 3. Then right-click on a .txt file (or whatever file type you want to open with ST3) and select Open with... - Choose default program... - Browse... and find sublime_text.exe. Now you can select Sublime Text.