How do you create a custom application launcher in Gnome Shell?

Try to create a eclipse.desktop file under /usr/share/applications (or ~/.local/share/applications or directly in ~/Desktop) with the following content:

[Desktop Entry]
Encoding=UTF-8
Name=Eclipse IDE
Exec=/path/to/eclipse/executable
Icon=/path/to/eclipse/icon
Type=Application
Categories=Development;

You can choose another category, too. For additional information:

• Gnome's documentation about desktop files;
• Categories available.

Although creating your own launcher by hand is a valid solution, my preferred one is to go through alacarte and create a new entry on the menus, then it will appear as a launcher.

In newer Gnome versions Comment and Terminal sections become mandatory so minimal .desktop file is now:

[Desktop Entry]
Type=Application
Encoding=UTF-8
Name=Sample Application Name
Comment=A sample application
Exec=application
Icon=application.png
Terminal=false